What is difference between 吃 and 在吃? Both of them mean eat/eating etc. So I am trying to find out purpose of the 在. Lingodeer app uses it almost in every sentence but Duolingo almost never uses it. So what is the right way or what is the right situation to use one or another?
You can look here in the new-look zdic for many uses.

For example sentences you can look here or here.

Often 在 is used with words like 上、下、里 as a double preposition. Watch out for that.

The difference between 吃 and 在吃？Not much and subtle! 

你要吃饭还是吃面？
Would you like rice or noodles?
我吃饭。I want rice.
我吃面。I want noodles.

我在厨房里吃晚饭。I'm in the kitchen eating my dinner.
我在吃晚饭。I'm eating my dinner.

你干嘛呢？What are you doing?
我吃饭呢！I'm eating!
你干嘛呢？What are you doing?
我在吃饭呢！I'm eating!