A mage with a major magical focus in Necromancy, wants to do a couple of things by magic I am unclear if it should be covered by the Major Magical Focus.
If we are talking about the canon MMF, the answer is no. RAW explicitly says Corpus and Mentem, applied to the spirits and bodies of dead people.
It would apply to Item 2 though, if we are talking about human bones.
Now, I do not think it would be an unbalancing house rule to extend the MMF to Animàl, but it would be a house rule. Since I try to minimise house rules in general, I would rather propose a «carnal necromancy» MMF for Animàl and Corpus, but not Mentem, than broadening the scope of a canon MMF: YSMV
I would take a generous reading and allow the first under a Necromancy focus, but not the second as it is merely bone working rather than animation.
The RAW description of necromancy does not refer to animation at all.
Corpus and Mentem as applied to the bodies and spirits of dead people.
As a Major Focus, I'd be inclined to allow animation of animal skeletons. It's still Necromancy.
I'm with loke. We have the definition of the canon MMF, and it's already large. I'd be entirely okay with doing an alternate major focus that would cover Animal and Corpus rather than Corpus and Mentem, but I don't think the focus should be extended to Animal, Corpus and Mentem, so I would be against option 1 unless the focus is redefined (easier to do on a new character than an established one). As to exemple 2, sounds like a corpus spell applied to the body of dead people (unless the spell carves and reshapes an animal bone).
Maybe extend to animal (animal corpus or mentem) but narrow the effect (dealing with the spirits of the dead or the reanimation of dead bodies)
That way you aren't using craft magic with human skin to bind books either, or human sinew for crossbow strings.
Oh thank you very much.
You have just reminded me that I have to check if the guidelines for manipulating Animal products can be used as a guideline for manipulating Human "products"....
Well, what about animating dead plants? I once envisioned a rather peculiar necromancer who created dead plants and then animated them.
I could accept Necromancy dealing with Co/Me and some other focus like (Re)Animation covering zombifying all manner of creatures and items.
That does not fit in my conception of necromancy as known in myths that I have heard.
There are many reasons for that
Well, I did say it was a bit of an odd idea - but it fits with the concept of animating dead, previously living things.
But by the same coin, a Co/Me necromancer could plausibly animate already living people, no? Even if it's not what they are known for. 
A Hermetic necromancer could do that, not because he is a necromancer but because he is an Hermetic Wizard who can do almost anything.
«Necro-» refers to death/the dead, so etymologically, animation of the living has nothing to do with necromancy.