To get appartment, you need a tech in civilization (don't remember the name). And I'm not sure the apartments are shown on the list iof available buildings in the tech (but you still get the buildings to build)

To get enough food you need one or two cities devoted to it. Find good places, build roads and a lot of advanced farming.

Can you be more specific?  I've upgraded civic and housing/estates several times and didn't see it.  I was wondering if anything else may need to be researched?  Or if I have to destroy all houses before I can build apartments, something buggy like that?

Jon, what I mean is that you GET the ability to build apartments when you research Housing.  I double checked this earlier; you get both Houses and Apartments with the Housing advancement. Apartments aren't an upgrade for the houses (although perhaps it should be!); it's a different structure.  You can't build the apartments in a city until it reaches a certain level, probably 4 according to Vieux.  And even then, the city must have four plots free because it's a big structure, like an Orchard.  As of Beta 1G, houses are never upgraded, AFAIK. Sometimes I have trouble building a second one, but usually not a first, try it again!

Or just wait until 1Z...it'll probably work differently anyway haha!

Farms are built on fertile land tiles.  You need to build your towns very close to such tiles to build a farm.  Same goes for apiaries and orchards (when researched).

Edit: But supposedly where the city is established won't matter as much in the coming new build as food will be a global resource shared by all your towns.  You will send pioneers out to establish farms on the tiles you find.

I just played 2 games and researching Farming and having the nearby tiles built (with huts i.e.) doesn't seem enough. Sometimes I can build orchards but not farms, otherwise neither...for a long time. When I pass my cursor on the fertile land tile, it still says in white "Needs Farming researched" when I already have Farming, Orchards and even Refined Farming.

And then I can build them.

I didn't exactly looked when and how it became available but: do farms and orchards require that the city be at level 2, or should I report this as bug next time I encounter this problem?

Yep it's a bug. Each game I play, I research civilization first to be able to build farms on turn 4 (or 5, I don't remember), and I always can build them the turn I get the tech.