1. I understand that there is no rule against starting a sentence with a conjunction, but I am a little unclear on when it is best to do so.
This isn't exactly true. Informal writing accepts this, but formal writing does not.
Which is of the following is correct, and why?
A) I wanted to see the movie, but I didn’t have any money, but it was okay because my friend paid for my ticket. No, you can't string two "But..." clauses together.
B) I wanted to see the movie, but I didn’t have any money. But it was okay because my friend paid for my ticket. Okay in the most informal writing.
2. I sometimes see people use a comma and speech marks to express their own thoughts, but I have never seen any rule that suggests you should do so. This is a matter of style. Some people use the quotes. Some people use italics. Some make it more like reported speech.
Which of the following is correct?
A) I thought, “We should buy one of these.” OK
B) I thought we should buy one of these. Would be better with a "that" to indicated the "reported speech" nature of the thought.
C) I though, we should buy one of these.
3. I have only ever heard the expression “[show] one’s true colors” used in a negative sense. For example, “He showed his true colors when he stole my wallet.” But can it also be used in a positive sense? For example, “His acts of kindness revealed his true colors.”
Already answered, but in my opinion, if you say "his true colors" it means that you have developed an opinion of someone and this opinion turns out to be false as demonstrated by later acts. Usually it's negative, but in the right context, I suppose it could work.
4. Is it fair to say that if you use the idiom “after all” at the start of a sentence, it can only mean “because ultimately” and not “despite what happened”?
Yes, or "when you consider the thing in total." It does not draw a contrast to what came before, as you would expect if using "despite."
5. If “support with love” is written as a title, do you capitalize the preposition “with”? Another style question. Usually prepositions and articles are not capitalized. It's an odd title. (And of course the S and L would be.)
If I have made any grammar mistakes when writing my questions, please highlight those for me as well.