Not-so-definite cases of comma use?

Hi. I could be mistaken but I think I have heard people say that short adverbial phrases when they come in front of a clause or are located somewhere appropriate within a sentence, a comma could, might as well, not be used. I think the example sentences below contain adverbial phrases, although I think the part "after some thought" is an adverbial clause. I think a prepositional phrase like the one in sentence number 5 "At his home" could serve as a adverbial phrase. If you asked me, I would say that I would not put any commas for all the example sentences below. I think the number 3 sentence contains an adverb, that is "surprisingly."

eg,

1.I felt enthusiatic and (comma?) upon receiving it (comma?) went ahead to teach.

2.I felt enthusiatic about the whole situation, but (comma?) to my surprise (comma?) Jane didn't feel the same and went home early.

3.I felt enthusiatic about the whole situation, but (comma?) surprisingly (comma?) Jane didn't feel the same adn went home early.

4.I felt enthusiatic about the whole situation, but Jane (comma?) after some thought (comma?) didn't feel the same adn went home early.



5.At his home (comma?) he was sitting on the sofa, sipping a cup of latte.

Also, generally do we tend to put commas more often when adverbial clauses that contain adverbial conjunctions that express surprise or contrast? I think I am somewhat contradicting myself by asking this question because I said previously that for example sentences one through five above, I would not put any comma anywhere, and to my knowledge the adverb "surprisingly" and the adverbial phrase "to my surprise" express an element of surprise.

eg,

I felt optmistic about the outcome of the situation, but Jane (comma?) although she is the person most affected by it (a comma?) didn't feel the same.