Yes it can sometimes mean that it is alright. He blew it off as nothing. You can take it as he said that his temper is not hot (he is not angry) about what had happened

Yes, your guess is right. It can mean "It is okay/all right. Don't worry" It can be confusing. 'Cool' has many different meanings. If you are confused by a meaning, check with an English/English dictionary, to see what other meanings a word may have. Here are all meanings for cool (The one in your sentence is #6): 1 fairly cold; not hot or warm 2 making you feel pleasantly cool a room painted in cool greens and blues 3 calm; not excited, angry or emotional 4 not friendly, interested or enthusiastic 5 (informal) used to show that you admire or approve of something because it is fashionable, attractive and often different 6 (informal) people say Cool! or That's cool to show that they approve of something or agree to a suggestion 7 (informal) calm and confident in a way that lacks respect for other people, but makes people admire you as well as disapprove 8 [only before noun] (informal) used about a sum of money to emphasize how large it is IDIOMS (as) cool as a cucumber very calm and controlled, especially in a difficult situation play it cool (informal) to deal with a situation in a calm way and not show what you are really feeling

It's cool here like it's ok = no problem .