My doubts arose after reading the section on Infinitives in the Oxford Guide to English Grammar by John Eastwood.
Part 1 of the question
Is it correct to generalize that all finite verbs change according to person, tense and number, while infinitives do not change? Or, are there exceptions? The book I have mentioned does not do that.
Part 2 of the question
In the questions "Do you play football?" and "Could you reach in time?", are "do" and "could" finite verbs and "play" and "reach" bare infinitives?
Part 3 of the question
"Can you reach in time?" Is this the present tense form of the question "Could you reach in time?" There seems to be a difference in meaning, "can" suggests possibility and "could" seems to ask about what actually happened. If "could" in this sense does not have a present tense, how can it be a finite verb form?
I went through the answers to related questions on this site but it is still not clear. Perhaps I do not understand some of those answers.