This is quite a simple explanation.
Duplets- for every beat, pick the note twice.
Triplets- for every beat pick the note 3 times
quads- can you guess the answer?
See...told you it was simple.
Your second question is going to depend on the song you are trying to play...
When you say 1234 1234 you are reffering to 4/4 time and yes you are correct if you are using quarter notes and the metronome is set to the speed of the song you are practicing.
If you're dealing with 3/4 (123 123)
2/4 is 12 12 12 12
1/4 is 1 1 1 1
It's been a while since I pulled theory out of my head, so if I'm wrong, please fill in the blanks.