Сделать тебе кофе?

[freiburg234.livejournal.com]

I've noticed that in Russian it is possible to formulate a question using an infinitive at the beginning of a sentence.

For example, "Сделать тебе кофе?" - Shall I make you coffee?

Can someone give me some insight into the range of possibilities of such constructions?

Is this construction, for example, limited to a few specific perfective verbs?

Can you give other examples of this construction in action?

Thank you in advance for your input.