[susan53]

A. The present participle can be part of a reduced relative clause - ie one where the relative pronoun and the verb BE have been omitted from a defining relative clause with the relative pronoun acting as subject :

i) I talked to the person (who was) dealing with the problem
ii) I hope we'll meet the deadline (which is) coming up.

This covers your example 2d: Nilson is the one (who is) sitting next to Yorky

B. The present participle is used after verbs of perception like see/hear/feel etc to express an on-going activity in contrast to a short activity, which is expressed with an infinitive. Compare:

i) I heard music playing in the background
ii) I heard the bomb explode.

In (i) it could of course be seen as a reduced relative clause - this covers your examples 1a and 2c, which use the verb see (NB it would be more usual to say I can see...). But that explanation doesn't explain the contrast with the use of the infinitive, and the use is restricted to verbs of perception.

C. Your example 3f is not possible. It meets neither of the criteria above: The original relative clause does not contain the verb BE (the girl who has... not *the girl who is having...) and the participle does not follow a verb of perception. The present participle cannot be used here and the sentence is ungrammatical.


I hope that answers your question.