Shadowverse

I got tired of "The Witcher" and stopped playing ranked.

I chose Gwent because of its decent visuals and familiar universe.

Everything is the same. I just got tired of Hearthstone too (a little later than "The Witcher"). Actually, now my interest in Hearthstone has returned thanks to the release of auto-battlers - I only log in for them, I don't even do daily quests.

I only read the first two books, and only played the first game.

Now I'm reading the fourth book and started the third game (in 2019, my computer finally allows it, lol).

Is it always worth pushing for a win in the first round?

I don't consider myself a very good player, but a lot depends on what you're playing. For example, if you have a deck with a super-powerful last move, and it's desirable that your opponent doesn't counter it (Glaive on Arachas, Squirrels on Gorde), or if it's very beneficial for you to go into a long third round (Northern Realms on Charges, Squirrels on Harmony), then it's better to win the first round so that you're not pressured in the second.
If you have a deck with just strong cards without focusing on combos (Northern Realms on the Marketplace, Nilfgaard with Knights and Turtles), then it doesn't really matter - depending on the situation, you either push or give up the first round. There are also decks that will throw out three useless cards in the first round and pass - there used to be Henselt, now I can't remember any like that right away.

Is there an optimal point difference at which you should pass to save your hand?

In my opinion, usually if you feel that your opponent can't catch up to you with one card (or vice versa - if you play now, and your opponent passes, and you won't catch up), then it's better to pass. Although not always)
Or when you have a very good hand, and you want to save all these cards for the third round, where they will be more effective. I often pass in such situations, and then I sometimes regret that I did it too early.

If you win the first round, how do you decide whether to push for a 2-0 victory or pass and save cards for the final?

It depends more on what your opponent is playing. If a long third round is beneficial for him, and not very much for you, then you need to push.
And also on your deck. Monsters on Larva (Fruits of Ysgith) and on Wills (Shadow of Death) almost always push in the second round because the ability allows it. Accordingly, it's better to try to win the first round against these guys - they will then be in an unfavorable position.
Or, if you're playing Syndicate and found Louise with Savolla, you can push until you have only these two cards left - and then in the 3rd round, 23 stats for 2 turns, balance)

Sorry for the long text, I hope I explained something)

Added 10 minutes ago

Am I considered an experienced player if I beat all the NPCs in the single-player mode of Gwent in "The Witcher 3"?

Gwent is now very different from what it was in "The Witcher," but I think in some ways, yes - many of the mechanics have remained. I feel like I'll be playing like that too (there needs to be a meme of Geralt reaching out - find Ciri - play Gwent, I just can't find it).