The Met = epic?

How do you define a heroic epic?

Looking at the Homeric epics and the Aeneid, it seems basically to constitute of a lengthy linear poem focussed on the amazing deeds of a main character.

What can the word "epic" encompass? Would it have had a strict definition in antiquity?

It can encompass hextameter poetry and sub-genres in general. No, it might not have done.

e.g: the didactic sub-genre or the heroic sub-genre

Who wrote the Catalogue of Women, which provided lots of stories about gods having sex with mortal women?

Hesiod (tho most scholars currently think it wasn't him).

Who wrote in the philosophical tradition, an offshoot of the didactic tradition? Would the DRN have been an epic of sorts?

Parmenides and Lucretius. Yes - the invocation to Venus at the beginning is very epic-like.

PROEM: Fert animus - what does this imply? Why does he mention the gods? Why does he say he is going from the beginning to the present time?

This implies that Ovid can write anything technically, but what he ends up writing depends on something very arbitrary. This is a nod to the heroic tradition. This is a nod to the Theogony.

What does Ovid mean to say when he describes the Met as a long, fine-spun poem? deductum perpetuum

This is not going to have 1 linear plot like the Iliad, but it is not going to be bitty and short like the Aetia. It possesses the same unity as the Iliad and Aeneid, but in a different manner. Crucially, the Aetia is written in elegiacs, and this is in hexameters, so Ovid is pointing out another difference between himself and his predecessor.

Where does Ovid seem to be working with the philosophical/didactic tradition?

Book 1 - discussion of chaos very similar to what Lucretius talks about.

What genres does Ovid incorporate into his poem that can't be classified as sub-genres of epic? Could you argue Virgil casts Dido and Aeneas as elegiac lovers?

He imports a lot of elegiac conventions into the Metamorphoses. Never to the same extent - Virgil is always serious and you could hardly imagine him incorporating the locked out lover trope into his poem!

How is love treated in the Hesiodic Catalogue of Women?

It is schematic and un-emotional

What does Housemann believe?

Hexameter poetry is the host genre, and Ovid is bringing in a lot of guest genres like elegy