Imperia Online International

What every of this building are needed for? Houses limit the maximum population size in the province. Farms=granary in v4 or is it something else?

Houses are place to live and you must have them so population will grow. When you reach limit, population stops totally.
Farms provide food to people. When limit is reached, people start to die slowly - that slows growth. Higher farms will push number of people much higher. They also give +1 villager growth. And they are both needed.

The 1 big difference is how you read you population growth. In classic and v4a you can only see what your pop growth is in people per hour. That figure would still be worked out in same kinda way. i.e in mountians/Forrest you have a -20% pop growth in classic and v4a and then + medicine, granerys and guilds(guilds only v4a) and this gives you your growth per hour you see in reports. But in V5 you get to read the whole equation instead of just the final figure. Once you get used to it. Then it will actually help you have a better understanding of how your pop growth is working. :)

Where can I find this formula or equation?

You have all explained in How to play. And you can see all info about it if you click on farm. Groeth, mortality rate, bonuses...

Click on farm: "Decrease population losses by 5% per level from the previous one given the bases 5400." What population losse r mentioned?
Look in HowTo: "Farm construction decreases the population losses due to shortage of food by 5% per level from the previous one, given the basis 7200 people." (and some words about increasing happiness after 5lvl)
But it is still NOT clear: What is the formula of those "losses".

It depends where you looked. Because Imperians and Nomads have different bonuses. 5400 is nomad number, 7200 is imperian.  You cant get formulas because thats in-game logic. But every lvl increase the number of people which dont starve or die.
Example: you have 100 k bonus from capitol. and you build lvl 1 farm for nomads. So your people dont die until you go over 105400 people. When you go over that, some people start to die. More people die as you go further from 105400 people. They dont actually die, so you dont lose population, but your growth will slow down. You will have growth lets say 200 and mortality rate lets say 50, so your actual growth will be 200-50= 150 people per hour. If you build another farm lvl, your people will start dying later.
Each farm lvl have 5% more people capacity then previous.

Thank u very much for your explanation. Therefore we generally no need farms until our population far away from 100K?

In capitol yes. But in other provinces you will need farms, they dont have 100 k capitol bonus.

This found in my second province:
Population limit    200 000
Current population    3 078
Population growth/hour    +57
 
Reaching limit after:    143 Days 22:46:19
 
Is it a bug?

You are nomad. You dont build houses. You have fixed population limit to 200 k.