If you total 21 before the dealer or any other player, you win the pot.
You can keep score according to wins, and determine the winning player by the number of games won. If you don't want to play for money, play for chips or for chores around the house. For most casinos, dealers are supposed to automatically stand if their first two cards equal to 17.
Some casinos, however, allow their dealers to hit on 17. On the table, it will say either H17, for hit on 17, or S17, for stand on 17. If a player is confident in their hand, they can decide to “double down” by doubling their initial bet.
After the initial bet is made, the dealer gives them one more card after which the player must stand. A player can choose to “stand” and keep the original cards dealt.
To have the best chance of winning, you should learn and practice "basic strategy", which is the mathematically best way to play each hand against each possible dealer upcard. Years ago, the only "Hit Soft 17" games in the US were in and around Reno, Nevada. Almost all other areas used the better rule of standing on all 17s.
If you are dealt two cards of the same value—let's say two 8s—you can split the hand. If you have blackjack, the dealer will take your cards, but you keep your bet. If you are not playing for money, you and the dealer are considered tied if you both have blackjack. Technically, scoring 21 with more than two cards is not considered blackjack, but you can still win this way.
Over the years, more and more casinos have switched to hitting soft 17, and there are now far more H17 games than S17 games.
A player who does not count cards should simply never take the insurance bet, even the "even money" variety.
Next the dealer passes out one card face up to all of the players and one card face down for their own hand. You are describing a CSM (continuous shuffle machine), where after each hand the dealer immediately puts the used cards back into the shuffler.
You will make more money on the pat 20 than you will trying to make two good hands from it. You will be required to make hand signals rather than just announcing "hit" or "stand" to the dealer.
Standing can be signaled by waving their flat hand across their cards. Starting with the one to the dealer’s left, players try to get their hand closer or equal to 21 than the dealer’s, without going bust. This can be done by hitting, standing, splitting, and doubling down. The dealer passes out one card face up to everyone including themselves.
If you have a blackjack when the dealer turns up an Ace, he is likely to offer you "even money" instead of the insurance bet. If you accept, the dealer will pay you the amount of your original bet and discard your hand of blackjack, before he even checks under his Ace to see if he has a blackjack as well.
Note that you are allowed to split any 10-valued cards, so you could split a (Jack, Queen) hand.
As you note, this eliminates the ability to count cards, or to even observe a useful bias. Since used cards can return into play immediately, the penetration is effectively zero. The only recourse is to see if your casino also still offers regular games (either hand-shuffled, or machine-shuffled but with a normal discard tray). What we have not talked about is how to actually make the best decisions while playing the game.