"I was busy with work." and "I was busy with some stuff." They're correct? Or ....
What would you say?

Question

"I was busy with work."  and  "I was busy with some stuff."  They're correct?  Or ....
What would you say?

Answer

Yes they are both correct. "I was busy with stuff" is more casual.  In England we use a phrase "I had a lot on." (as in I had a lot on my mind).

Answer

Yes they are. 
You could also use "I was preoccupied." (pre·oc·cu·pied )