I know vaguely what it means, somehow 'even' or 'at least' but I would appreciate some examples of different usages of the word, so that I can start using it by myself.
Also when do I use έστω as a one word answer?
Used by a person talking when he/she agrees or consents to something happening even not to their full satisfaction. So, it means “Let it be / I am ok with that”. In this case, it can be --and usually is-- used as a one word answer.
Έστω can also be used at the beginning of a sentence followed usually by a ότι + verb sentence. In that case it means “Let's say / Suppose that …”. This syntactical structure also has a special use, as it is often used to introduce math problems.