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Firstly, I want to know whether will have and shall have are modal verbs, or do they have future perfect tenses, or both?
If these are modal verbs, can I use them in both the past and present?
Secondly, can I use may have in both the past and present?
will have is a way of discussing the future or future intent, either: (a) with respect to having something, e.g. "I hope they will have fun this evening", or (b) followed by a past participle, to form the construction known as the future perfect, e.g. "after two more years I will have lived here for five years".
There's also "will have to", which expresses future obligation, e.g. "I will have to give him a call". (It's future in the sense that you haven't called him yet, but the obligation may already be felt and sometimes it may require fulfilling imminently.)
shall have has similar uses.
"Will" and "shall" are modal verbs. "Will have" and "shall have" are not modals. Rather, each consists of two verbs, one modal ("will"/"shall"), the other non-modal ("have").
You asked, "If these are modal verbs, can I use them in both the past and present?"
I find it difficult to see how you can use "will have" and "shall have" to discuss anything other than the future - although in the case of "will have to" the obligation may already be held, and in the case of "will have" + past participle, you may already have begun but not completed the action, as in "if I score two more points, I will have won this game".
You also asked about "may have". Yes, this is also a valid expression. It can be used in various ways:
Firstly, you should not say "Firstly", secondly, will have and shall have mean the same thing: in the future you will have something.
May have means the possibility of having something or having done something, or it can be used when asking for something like "May I have an apple?".
the prof. said: "You will have five minutes to answer the question."
shall means the same of will but old-fashioned.
May I have your name? equals what's your name?
she may have a bf already I said to my fellow. == Sha maybe has a bf or not, 50% respectively.
in all examples above, May Will Shall are model verbs and Have is just a verb.
Modal verbs are will, shall, and to have only, not their combination will have or shall have.
(So your another question “If these are model verbs, ...” is irrelevant.)
To answer your last question, may have is never used in the past tense, only in present or future (e.g. in the form may have to) ones.
