L'avrò chiamatO tutta la settimana. => I will have called HIM all week long.
L'avrò chiamatA tutta la settimana. => I will have called HER all week long.
This was covered previously in the Clitics section (ARRGGGH! Bad memories).
In the compound tenses, the past participle must agree with the third person direct object pronouns ("lo", "la", "li", and "le" ) . Agreement is OPTIONAL for "mi", "ti", "ci", and "vi".
The pronouns "lo" and "la" become "l + apostrophe" before a vowel: "l'avrò".
The pronouns "li" and "le" do not elide: "Li avrò chiamati" and "Le avrò chiamate". Good question!
In regards to past participles: "It's endings have to agree with the subject (in the case of verbs taking the auxiliary essere) or sometimes the object of the verb..." Taken from "Modern Italian Grammar" by Proudfoot and Cardo. There you go clear as mud. I think that with essere past participles agree with the subject and with avere they agree with the object.
The word "long" at the end of the sentence is superfluous; in English (at least in American English) we would say "I will have.... all week" The extra word "long" is implied and would typically be omitted. The phrase "tutta la settimana" is typically translated as "all week" or "the whole week". My answer should not have been marked wrong for omitting "long".