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Question 1: Is it correct to check after the river card?

A: Like a lot of poker questions, the answer to this one is a rousing, "it depends." The reason many good poker players check certain hands on the river, even good hands, is that they know that the only way they will be called is if they are beaten. If you bet on the river with the best hand, and everyone folds, your bet gains you nothing, because you would have won the pot anyway. Generally (and I do mean GENERALLY, not always), when you bet on the river, you should either have a very strong hand (which can be called or raised and still win) or a moderately weak hand (where by betting, you are trying to buy the pot from a player who might also have a moderately weak hand, perhaps better than yours, but not good enough to call a bet with). Another reasonable reason to check the river is if you have been pushing the pot the whole way, and have such a monster hand that you are afraid everyone will fold, and so by checking and showing weakness, you might induce a bluff and steal an extra bet.