You'll find that most people - especially low limits - will only play their own cards. There's nothing wrong with this, but once you know what their value of certain hands are, you will be able to find the likelyhood of their holding a hand which is dangerous for you.

I generally make a lot of notes. It keeps me concentrated on the table because it's easy to be distracted with so much to do online. I like to note what hands players show down and how they played the, Did they limp AXs from EP and then call pot bets on the flop and turn to river their flush? Maybe they raise any suited connectors PF?

If you flop the nuts and give a free card, then you may as well bet it out. If you can get an active player to come along with a half pot bet, then great, but generally players will only come any further if they like their hand - whether you have the nuts or not doesn't matter greatly at this point.

If you flop a set and are called on the flop only for a scare card to come, what is the likelyhood of them holding the hand you're scared of? Would they have called on a gutshot, have you seen them chase before? Would they play TPTK the same way, and how about second pair? If you're out of position I think a bet is still correct. Do you want to announce that the turn card just froze you in your tracks? Some students of WPT will call with anything on the flop to see how you react to this, and I've taken down bigger pots by just grabbing my balls and betting again.

Checking if you think they have it is fine. Some of them will go all in for 4x the pot and depending on the player you can take down a large pot with any pair here. I also bet the flop on the draw to those hands which you would be scared of in this situation, and then check when they hit. If (in the unlikely event) your opp pays attention, and you can keep them confused as to your holding, all the better (although it must be said that a lot of them don't care what you have - this still keeps you a few steps ahead of them).