I have this kettle that looks something like this
It has quite a lot of space for coffee and not so much for water (I am filling them up both to max).
Is it intended for coffee to be re-brewed (water changed) or I should change beans every time?
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The photo you have posted is a standard moka pot (See Wikipedia entry here) by a well-known brand, actually the inventor of the moka pot.
You should fill it up to the safety line. You should see it when you fill it. That line is generally curved inside. Filling it more than this line may cause high pressure due to evaporation of water and it may cause harm.
This equipment is not intended to re-brew coffee, but to brew coffee that tastes similar to espresso on the stove. (8 grams of coffee per 30 ml of water is the common accepted ratio.)
If you are interested in re-brewing used coffee grounds, you may also check this related question: Brewing with the coffee grounds twice?