Empire: A chronic shortage of food no matter what?

Food in general seems to be messed up, sometimes I am lucky and get a settlement with 2 fertile tiles, then its ok.

What really needs to be done is each settlement needs to have a default food production amount at a given city level to support defense forces and the population.

Bonus fertile tiles where "large scale" farms are built would be for army and further defensive force expansion.

City level 1  =   +1 food

City level 2  =   +1.5 food

City level 3  =   +2 food

City level 4  =   +2.5 food

City level 5  =   +3 food

Something like that maybe ?

I haven't played with the empire much, but does the Domination thread have the ability to discover new resources such as gold and food? When I play as Kingdom, two of the first things I research are Adventure to somehow "discover" new resource tiles.

yep , I know you can discover fruit orchards for sure, 25% food bonus if I recall...

Empire gets less food and more gold.

Well, not only can you find more resources, and research better food production, but the problem usually happens when you take over enemy cities. For some reason, so far the AI doesn't seem to always need food, and they place cities all over the place. Capturing them can decrease your available food by a lot.

And since food is a scarce thing, you have to be really careful about placing cities not next to a harvesting place.

Besides... you're supposed to be low on food, remember? Part of the environment 

I don't play Empire a lot either.  Generally speaking, it varies.  One thing you have to do is to be careful about when and where you build the population-increasing improvements (huts, etc.).  If you don't find alternative food sources, you could be in trouble.  I USUALLY do, but then again, playing kingdom, you can get those fairly easily.

I always tend to play Empire and until now I had never any real problems with food, even if I had 20+ cities of lvl 3+.

There isn't much to do other than picking three or four cities to specialize on producing food. There you do the following:

- Use both building with the +25% food production
- Use as many caravans as possible to increase the food output
- Try to get a few of those champions who give each a bonus of +20% and put them in the city with the highest output

With this I usually get each city to produce something around 20 - 40 food and more, which can keep many other cities running.

Other than that, even without caravans you should use every oasis and fertile land, for a few of them can also sum up in a nice supply of food.

One last thing: There is no need to bring any city above lvl 3 but two or three at most, since Empire has very few building requiring a higher city lvl. Three or four houses are enough. And destroy the huts in conquered enemy cities - the AI is fond of building way too much of them.

I've only played Kingdom. But I research the food techs under the civ research and also research adventure techs to discover more food resources. Also, I don't overbuild houses.

I usually raze enemy cities unless they're in a good location.  The AI will sometimes put cities the minimum five tiles away, for no other reason than to grab a clay mine or other useless resource.  And currently, since one stack of squads can march across the land and bludgeon everyone to death (and the AI likes to leave Sovereigns unprotected) I don't do defense.

And razing things is just fun anyway.

Don't expand unless you absolutely need to. Unlike other games, there's no huge benefit to doing so - the 20% bonus from level 2 is not going to make up for the -1 food (25%) needed. In fact, since a level 2 requires 1 food, jumping to level 2 to get a food bonus does not actually help! A farm makes 4 food. It takes 1 food to level up so now you have 3. Building the 25% farming bonus building gets you back up to 4 food. In essence, you're spending -1 gildar per turn for not actual increase. 

Where the food production bonuses help is when you have a high base to begin with (anything that gets you more than 4 food). In that case, you have a positive growth on food initially. If you don't, then it's better to keep the city at level 1 and use caravans to boost food production first.

The Empire gives up the bonus food tiles in the adventuring tree for an extra caravan per settlement.  Generally this means you're going to be more food constrained in the early game, but less as the game progresses.  My typical remedy is to go capture a Kingdom capital ASAP.  Of all the basic resources in the game, Food is the one I have never had any shortage problems.

Are food bonus buildings (like+25%) added before the buildings that take things away or after evenry thing is equaled?

Before.  A city that produces 4 food, has two houses, irrigation (+25%), and medium length caravan (+50%) nets out at +5 food to the global pool.