Question

Namely, for instance, when I say:  She gives to him a gift, or with other verbs. Is the preposition an obligation in some verbs?

Answer 1

with ditransitive verbs, u can always omit the preposition if u put the indirect object (the recipient) first. e.g. give me the ticket, build me a castle, order them some spaghetti, etc.

Answer 2

why not say it simply into: She gives him a gift.

If you wish to know more about the preposition "to" be sure to check this slide:

 

http://www.slideshare.net/stephlowe91/ielts-grammar-prepositions