As you don't remember every detail, your question is a bit imprecise. So let me answer with some generic arguments.
Preflop. You have to be a bit careful: you are in the small blind and Villain, in the big blind, has position on you. Since you have the feeling that Villain folds too easily, you decide to steal the blinds by raising to 6c. Why not?
However, I ...
Agreed with UC—there are some starting concepts you're still working on, and you're making things way too hard on yourself by consulting hand calculators and working out equity positions. That's for later, when you have a breakeven or slightly winning game and you're looking for your leaks.
If the opener has a wide range from the cutoff, when he c-bets the ...
By your use of terminology, I will assume you are a newer player to the game.
You’re thinking along the right lines and I think you’re reading your opponent correctly. But you also have to think about your own actions and what you’re saying.
The action you described - without you even knowing :) - is called a “stop and go” and it’s considered to be super ...
I do think you can even consider folding just because of his sizing on the flop, but as played I would mix in some raising and folding on the turn.
You clearly can't be calling here, and since you have quite some equity and some good bluffing runouts like any diamond, raising like half of the time and folding the rest seems like the best option.