This is a good question!
Part I:
The difference between 'she' and 'her' is possession. 'She' is the same as 'ella' in Spanish, while 'her' is more like 'su' - but has a feminine gender.
Part II:
This one is harder. Here, the first sentence has an independent clause and a dependent clause. I will break the first sentence up into the two clauses, but it may be a little confusing. Tell me if you would prefer me to rewrite it.
It was them (An independent clause - in this case the verb object is 'them').
who called this morning. (A dependent clause - this clause, while a complete sentence, does not express a complete thought in this example.)
'Them' is used as an object of a verb - in this case, the object of the verb 'to be'.
The second sentence is much easier, because it is not a complex sentence. 'They' is the subject, and it is used because of a rule in English called 'subject-verb agreement'. This means that the subject's tense and number must agree with the verb's tense and number. 'Were' is the plural form of 'was', and 'they' is a plural noun that indicates that the speaker is not a part of that group.
I hope that helps. English grammar is confusing (especially subject-verb agreement) even for native speakers. I had a very hard time with it in college.