Minfeng writes as follows, I assume from China. He or she (I can never tell with Chinese personal names) is clearly oriented towards BrE rather than AmE; I have adjusted the phonetic symbols to those I customarily use.
1) In the strong form, the pronunciation of "to him" is /tuː hɪm/; but when it's in the weak form, is it /tu ɪm/, or /tə ɪm/? I think it's /tu ɪm/, since /tu/ is used instead of /tə/ before vowels (/ɪ/ here). I would like to know whether I am right here?
2) If I'm correct with 1), I assume that the weak form of "to her" is /tu ə/ instead of /tə ə/.
3) Should I pronounce the weak form of "for him" as /fər ɪm/ since "for" is followed by a vowel (/ɪ/, but not /h/ here)?
4) Same as 3), should I pronounce the weak form of "for her" as /fər ə/ (but not /fə ə/)?
My answer, perhaps too laconic, was
Just follow the rules.
Of course, it’s a little bit more complicated than that.
First, a phrase such as to him or to her does not as such have a strong form or a weak form. Rather, it is the individual words making up the phrase (i.e. to, him, her) that have strong and weak forms. It is perfectly possible for the preposition to be pronounced strong and the pronoun weak, or vice versa (for some discussion of this issue, see my blog, 1 October 2009).
Secondly, in real life the weak forms of him and her do not necessarily involve dropping the h; and the weak form of her does not necessarily involve weakening the vowel from ɜː to ə. That’s why in LPD I give the weak forms (sic, plural) of him as hɪm, ɪm, and the weak forms (sic again) of her as hə, ɜː, ə. (Let's ignore the question of whether the strong-vowel variants can truly be called weak forms, and overlook the fact that ɪ is sometimes a strong vowel, sometimes a weak one. I'm talking about the forms used in positions where on other grounds we expect a weak form.)
Thirdly, in real life it is not unknown for speakers to weaken to to tə even before a following vowel and/or to fail to use a linking r with for. So in real life you do sometimes get pronunciations such as tə ɪm, tə ə, fə ɪm, fə ɜː. Nevertheless, EFL learners are recommended to follow the rules as given which will always generate an acceptable pronunciation.