Depends on what you mean by "faction". There's two sides, Kingdoms and Empires. Those two sides have unique tech trees, different buildings, and other differences.

Within each side there's five organizations, which is what you probably mean by factions. Those have some differences in terms of specialities and such, and some of them on the Empires side are non human. If you're looking for things like Elves/Dwarves/Hobbits, you won't find them.

Yep! As of beta 4 there was quite a few, some of which could only be found in game. Don't know if that's changed in release yet.

It's more important then in Sins, but I haven't played much with the diplomatic side of things yet.

Functionally those two games were doing similar things, since the "little groups" acted as one unit for movement and commands. Elemental is like that. You can train a group of 20 soldiers and there's 20 of them, though they act and move as one. You can also have individual units like champions and the sovereign that are much stronger.

Yes there are no elves, dwarves, hobbits, however there are "Magnars which are known as 'Demon Elves' in the common tongue" and "Urxen, sometimes called 'goblins' in common". Both quotes taken straight from the Elemental lore page.

But they don't look like traditional goblins or elves from AD&D... the different factions/races are more like blue-skinned humanoids, or red-skinned humanoids, or a gothic looking human.

To answer the OP questions: It's fair to say there are 2 main sides, Kingdoms and Empires. The further subdivision of factions don't seem to have the same degree of differences among each other as the 2 sides do (or at least the documentation hasn't been stellar in pointing out the differences so far). Yes one faction within a particular side may build roads faster and have 20% slower research, while another faction has a  boost in combat performance, and another faction gets a different small bonus/drawback and they're as differentiated as the different Civs are in Civilization. (A 10% boost here, -20% there, and perhaps a 'bonus unit'). I don't find the factions to be as differentiated as races in other fantasy TBS games or other IPs.

Factions don't have different army types to draw upon per say. You design the units based on tech. you research. For example, you discover a sword tech, and you can then build units equipped with swords and call them "swordsmen". Each faction that  can discover swords (or any other weapon type), can build swordsmen. There may be some weapons that are unique to a faction/side but otherwise your more limited by your weapon tech as to what you can build. A lot of techs are shared by factions.

As for tactical battles. No one but the devs has seen tactical battles with unit special abilities, etc. and the beta tests have just had bare-bones battles so it is not fair to comment on it yet. Objectively all I can say so far in reference to AoW and MoM, is the tile-based combat board is smaller than the tile-board in MoM. How it plays out in the final build, what the tactical depth is, etc. is unknown to anyone outside of the dev team.