In the first game, the time control was 1 day per move, so the timer resets each time you make a move.
For the second game: Here's an article on how vacation works
https://support.chess.com/article/624-how-does-vacation-work-how-much-time-do-i-get
There isn't an option to reopen a game that is over; however, you can play a new game a agree on playing out the exact same moves you played in the other game up to the point where you lost on time, then go from there.
Dear Chess Support Team,
I joined chess.com, few days ago. I am brand new to playing chess with few hours of online guides as experience. A classmate challenged me (she's 1400 rank), I'm ranked 500. Both games we played she set the timer to 1 day. On our first game, we played casually for three days and I ended up winning. I wasn't sure why after 1 day we could still play? I thought it must of been some kind of glitch. I earned 500 rank and shot up to 1000. I was very happy. Then on our second game (which I was winning once again), I had a lot of homework to do so I didn't check chess.com at all that day. Remember I'm still a new player and not sure of rules and or "vacation time" even exists. The next day she sends me a private message on Discord saying "Good game." I reply with "?" then she says "I won on time" and I reply with "good game" out of sports man ship. Later I get home and it says she won. I find out that its 1 move a day to continue the game? I'd like to please REOPEN this game, thank you. I am still learning and would like to know what the final outcome of this game would have been.
Request: Reopen match
Reason: New player did not fully understand match rules
Match: https://www.chess.com/game/daily/386266289
Regards,
Douglas