Yes, Joyce gave great feed back. Generally, shed a tear is more formal and a grand statement and crying is a more general term. It really tore me up (past tense) or I'm really torn up (ongoing present sadness)- it's a difference in tense. I did not shed a tear (past tense- exclamation) when my dog died... is something wrong with me? I tear up when I see a sad movie (conditional... future tense). Hope this helps!

The verb is the same. We say, "shed tears" or "shed a tear". The form of the verb depends on the subject, so you could say, "She sheds tears every time she sees that movie." or "We shed tears when something makes us sad."

Definitely not 'He tore up / He torn up'. 'He teared up' is used, but is a little colloquial, and unusual. You could also say 'tears welled up in his eyes', before they actually fall.

I think I should have said that "tears" or "a tear" shows the level of emotion, to "shed a tear" is less emotion.