That second game in the totally locked up position looked really tough but I think you were handling it well.
Rehan's Beginner Study Plan

Week 5 Update:
Daily - 1471 (+15)
Puzzles - 2120 (-16): Did not calculate accurately while attempting puzzles. Funny thing was that most of the times when I got a puzzle right I only gained 5 points while when I failed I lost more than 10 points, that does not seem fair.
Rapid - 1200 (+18): Well I am half way through the study plan and have already reached my rapid rating goal as well as puzzles rating goal, so I am happy about that.. Now I just have to keep playing good chess, maintain my current rating and this study plan can be counted as a success.
Blitz - 703 (-5): I was not planning on playing any blitz but someone challenged me and I did not want to decline so I played two games and lost both of them..
Learning Material:
Chess.com Lessons: Capturing pieces, Finding Checkmates

Congrats on reaching your Rapid goal!
The puzzle point system is frustrating. To spend the time to calculate means you do not get the full amount and as you note, only 5pts. But if you miss then you lose them all. I suppose it makes sense, but it is frustrating and has fueled my multiple puzzle binges that torpedo my rating.

Yes, I agree that the puzzle system is quiet frustrating. Chess.com is actually about to release a whole new system for puzzles that will hopefully feel better.
Under the current system, you can earn "full" points for solving, but only if you solve it stupidly quickly. I think the rating system for puzzles is kind of broken as is. I understand we need to rate puzzles to be able to serve people puzzles that are challenging, but I hate adding in the frustration of losing rating to something that is already difficult.

Week 6 Update:
Daily - 1474 (+3): I have started some daily games with higher rated players to improve my daily rating using the help of open challenges section. Previously I was mostly playing in daily tournaments and got matched up with lower rated players, so the rating gain as well as the learning experience was not that much.
Puzzles - 2128 (+8): I feel like I am stuck at my current rating. I am planning on reviewing the puzzles that I have failed so that I can reinforce the tactical themes.
Rapid - 1200 (-)
Blitz - 749 (+46): I could have done much more better. Some games I lost because I did not calculate accurately while some I lost because of some connectivity issues (which frustrated me a lot).
Learning Material: According to the study plan, I had to work on openings for 45 mins but I could not think of good ways to do that as I had already finished opening lessons in the chess.com guide, except for the "Key Openings" Lessons in the advanced section. I went through the first lesson in it but it was very broad and covered a lot of off-beat openings in a single video. Did not get much out of it because first of all I do not get that many off-beat openings in my games and secondly when I do get them, I know that I have to follow the opening principles, develop my pieces and I can get a good position.
I perused through the book recommended in the study plan for openings, Winning Chess Openings by Yasser Seirawan as well but that is also structured as an encyclopedia of openings and I do not think I can benefit from it that much. It's too much knowledge for various openings that I will never use.
Next time, on opening weeks I will try to go through my own games to understand my opening weaknesses so that I can improve on them. Another option would be to learn about specific openings that I do play and work on my opening repertoire.

Week 7 Update:
Daily - 1482 (+8): Score +1/-0/=0 Managed to win a game where my opponent blundered his knight and I converted it effortlessly.
Puzzles - 2123 (-5): I have come to realize that it would take a little bit more time to increase my puzzle rating further. I need to be patient and understand the patterns that I am unable to get. Another thing that I have realized is that the puzzle scoring method on chess.com is based on the logic that if you cannot solve a puzzle within 1 min then this means that you do not recognize the pattern therefore you do not get the full score. The main goal is to recognize and internalize more patterns. I realized this after watching this video on chess.com.
Rapid - 1181 (-19): Score +7/-8/=0 I lost 4 games because of either internet connectivity issues or because I had to go for an errand or something and in most of those games I had a winning position. If I want to improve my rating I would have to ensure that I am not disturbed during that time. During other games, I was able to get winning positions but I failed to convert them because I did not consider my opponents threats and instead was focused on my own attack.
Blitz - 749 (-)
Learning Material:
Chess.com Lessons: Every Sacrifice to Destroy Your Opponent by WGM Keti Tsatsalashvili
Chess.com Videos: 4 Exercises To Become A Tactical Genius Part 1 and 2

I lost 4 games because of either internet connectivity issues or because I had to go for an errand or something and in most of those games I had a winning position.
That is great to recognize that! Your rating is not always the best indicator of how well you are playing. I tend to measure my progress more on the accuracy score than my rating.

Losing due to things beyond your control is frustrating for sure!
I think your plan for Openings is a good one. If you play a typical opening, going back to your games and seeing where you got off track is a good way to learn those next few moves.

That is great to recognize that! Your rating is not always the best indicator of how well you are playing. I tend to measure my progress more on the accuracy score than my rating.
Yeah! accuracy is a very good indicator of gameplay. The new report card feature on chess.com game review also breaks down accuracy for each phase of the game which is quite helpful and interesting.

Week 8 Update:
Daily - 1482 (-): I have got some daily games going on.
Puzzles - 2139 (+11): Along with the rated puzzles I am also trying to go through the puzzles that I have previously failed and if I am not able to solve them then I go through them several times to understand the pattern behind the puzzle. I think that this would be peak puzzle rating for a while.
Rapid - 1179 (-2): I mistakenly started a rapid game although it was Blitz week. I had winning advantage through out the game but I failed to capitalize.
Blitz - 743 (-6): Score +12/-13/=3 I lost games due to bad opening play, sacrificing without accurate calculation and missing opponent knight forks that lost material.
Learning Material:
Silman's Endgame:Part Two Minor Pieces vs Queen. Tried to find drills related to the topic on chess.com but couldn't find any so tried some other endgame drills.
Chess.com video: Solving the Problem of the Queen part 1.
Week 4 Update:
Daily - 1456(+16): Game Score +3/0 One of my opponents was close to my rating level (other two were as usual lower rated than me), I enjoyed playing that game a lot. My opponent surprised me with a fork on my queen and rook but I managed to find a useful resource in that moment to win the game.
Puzzles - 2136(+171): Getting good scores in puzzles. Have been doing puzzle rush as well before each game to increase my focus during the game, which has helped me a great deal in improving my rating.
Rapid - 1182(-): Next week is rapid games week, last time I went overboard by playing a lot of games and failed to analyze my games. I intend to change that and play only 2 rapid games in a day and concentrate more on analyzing my games.
Blitz - 708(+55): Game Score +17/-12 I am enjoying playing blitz games. It provides a nice change of pace and I feel like it has helped me calculate a lot more faster and see things more clearly when I get back to Rapid games. I can appreciate the extra time available during rapid games after playing blitz games in a harried manner. Of course, I make a lot of blunders and feel silly after analyzing games.
Analyzing blitz games seem less fruitful because at the back of my mind, every mistake can be attributed to lack of time.
Learning Material:
Silman's Complete Endgame Course Part-1: I already knew how to checkmate with the Queen and King as well as Rook and King but I had a good refresher. I also completed some endgame drills on chess.com to review the concepts.
Chess.com Videos: Achieving Full Board Awareness. Have removed the coordinates from the board on chess.com to memorize the position of the squares. Have started Vision Training on chess.com.
Youtube Videos: I am trying to learn how to analyze my games better so have been looking at youtube videos on analyzing and annotating games. Previously I used to go through the chess.com Game Review feature and retry any mistakes and blunders but now after watching some videos, I think I should analyze without engine help first, annotate my own thought process during the game and use game review feature / engine analysis afterwards.