Main verb in a sentence and gerund

In the sentence "Offering her license and registration, Selena sobbed in the driver's seat," offering is not a gerund, right? It isn't a noun and does not act as a subject. That made me wonder if the main verb is offering or sobbed.

I'm having a hard time trying to identify the main verb and phrase verb. Actually I'm wondering if in my last sentence the main verb was trying or identify.

One last question: In the sentence "The man is watching the birds," is the main verb watching? or is? and why?

Please, any help is welcome.

"Offering her license and registration, Selena sobbed in the driver's seat."

No. The subject (noun) is Selena and the main verb is sobbed.

I'm having a hard time trying to identify the main verb and phrase verb.

The subject is "I." The main verb within the predicate is "having". The auxiliary verb (the one that's helping the main verb but does not describe the action performed by the subject) is "am."

The man is watching the birds.

The main verb is "watching." The auxiliary verb is "is."

You also asked for confirmation that offering is not a gerund. You’re right, it is not a gerund, but a present participle verb heading the bracketed participial clause. Notice that it has her license and registration as object. This kind of clause is very common; it’s often referred to as a supplement, detached by intonation or punctuation from the rest of the clause. Supplemental clauses offer useful but non-essential information, and as such are omissible with no loss of core meaning to the sentence as a whole.