When should you use "then" and when "than"?

Because I'm older than she, I should be the first chosen.

I loved her and then she died.

If it rains, then it pours.

I've had more than enough.

Would you rather be a mouse than a rat?

Who, other than you, likes the color red?

When there is a comparison, you use than; then means:

1. at that time; at the time in question: I was living in Cairo then | [after preposition] Phoebe by then was exhausted | [as adjective] a hotel where the then prime minister, Margaret Thatcher, was staying.
2. after that; next; afterward: she won the first and then the second game.
   • also; in addition: I'm paid a generous salary, and then there's the money I've made at the races.
3. in that case; therefore: if you do what I tell you, then there's nothing to worry about | well, that's okay then.
   • used at the end of a sentence to emphasize an inference being drawn: so you're still here, then.
   • used to finish off a conversation: see you in an hour, then.

(See also the definition of then given in the Oxford Living Dictionaries.)

Two corrections:

• I’ve had more than enough.
• Would you rather be a mouse than a rat?

Both “rather . . . than . . .” and “more than” are fixed expressions.

Then is time related, like you said. It divides two (or more) occurrences. Example below.

Jack went to the shop, then he went to his grandmother.

Than is a word we use when comparing something. If something is more or less than something else. Examples below.

Jack is stronger than Cole.

.

Cole is weaker than Jack.

Also, then is always preceded by a comma or an "and" (unless you're speaking about the word itself). Than is never preceded by a comma.

Hope I was clear enough.