Does analysis interface improve, when I buy membership? How much better is it?

Let's say that you play a game and want to analyze it later. Let's say that there's a moment, where you are not sure about the next move, example from my quick game:

I decided to move the queen (Qd4) and my evaluation dropped by about 0.6 (actually much more, after letting engine think about my former position, I dropped like 0.8-0.9!).

So, wondering what I should o here, I had to switch to engine analysis.

On another site you have multiple arrows and lines, even during analysis, that show you the best moves in current position, but here on chess.com we have nothing like this. No arrows, no hint, no saying what's the best move, unless you make blunder/mistake/inaccuracy, so you have to switch to the engine.

What's bad about it? Well.... it resets your whole analysis!!!

So, every time I want to check what the move would be better, I have to switch to the engine, which resets my analysis, so I have to wait another 2 minutes for a new one, then when I encounter another move I am not sure, I have to switch again and wait another 2 minutes for next analysis... and so on...

This is not only really bothersome, but even ridiculous...

I think that sometimes it works and don't reset my analysis, but it works like once. Then, it keeps resetting it.

So, my question is:

Does it change, if I buy membership? For me, how analysis looks like, completely sucks... you not only can't check the best moves, without changing over and over to the engine (why the both of them can't work at the same time??), but the analysis also keeps getting reset, so you have to make it again..

I am really thinking about buying year long subscription, but how the analysis works like scares me out a little and discourages from doing this :-(

I didn't tried trial yet, as I have no time for chess in next week or more and I would simply waste it, so I don't really know how it works like with membership.

Is it the same bad in terms of user interface? Do you always have to keep changing into engine analysis (self analysis), or maybe you can do both at the same time?

If you buy membership, can you check the best move possible without leaving analysis? Are they maybe somehow visualized, in similar way you have on lichess?

How good are deeper versions of server analysis? I noticed that after just few seconds, or even less, of self analysis, Stockfish gives much better evals than 2 minute analysis of 50 move long game, so I suppose that server analysis isn't really strong and the difference is just in more time assigned? Does it mean that on my laptop I can make similarly strong analysis to the one that server gives me? On would think that server should give you much stronger one, but looking at the quick analysis results and that deeper ones only increase the time, it doesn't look so?

I would be grateful for a help :-)

As premium, once you run an analysis, you can save it. 

Also, all analysis is run client-side.