how many villagers i must put to harvest the crops?
is there faster we harvesting crops = the early crops will be reseed (replant)? and how many villagers to put to get the fastest research? is there a limit?

The crop cycle is on a set cycle. It does not matter how fast or how slow you pick the crops. You will find that if you still have half your crops in the field, when you get a new crop cycle the garden will be full again. And the cycle time stars as soon as the new crops popup, and not after the last turnip is picked.

And there is no limit on the number of villagers you can put on research.

But if you don't pick all of the crops before the next crops appear, you'll lose the ones that weren't picked (they spoil). It's best to make sure you get them all picked if you don't have a lot of food in the bin.

Much depends on two things: the speed at which you are playing the game and how many villagers you have. One villager can comfortably serve as farmer during the early stages of the game (up to about 20) but you will need more as the population increases. The crops appear about every two hours if you are playing at 2X speed, and correspondingly slower if you are on a slower speed. That is usually enough time for a single farmer to clear the field but if you notice there are still a lot of crops left towards the time when another crop is due you might want to put other villagers on harvesting to make sure none of the crops are "wasted".

The more villagers there are on research the more the tech points are accumulated. There is no limit. However, it also depends a lot on the experience of the villagers: a trainee earns far less tech points per completed science task than a master. Also, it depends on the tech level, with those on L3 science earning far more a "turn" than when the village was at L1.

Do you suggest one farmer for every 20 people or more when the population grows? Like one for every 15 people?

Each person consumes one food unit every two minutes, at 2x speed.

So farmer would need to collect 40 units every two minutes. Each trip adds about 10, and he wouldn't be able to do any laundry.

I think one farmer for 10 people (2 for 20) would be about the minimum at 2x speed.

I generally have little difficulty using one farmer for up to about twenty people (at 2 X speed) but it's important to keep a close eye on the situation. I try to train villagers in a variety of skills so that they can slot into another job easily if need be.