Give
To give in is sort of like to give out. Giving in is surrender and is closely related to giving up, which is to stop trying. To give out is to lose the ability to hold on, as in the road gave out from the flooding. Interesting to note the relationship between in and out here. In has the suggestion of opening and welcome, as in come in. Out is an opposite as in get out. So give in might be more welcomed than give out
To give is different than to sell. If you give to me, the act is a gift. If you sell to me there is a contract, an understanding, about the transfer and about who then holds responsibility, when. That responsibility could, at a lesser level, remain with some gifts, say, something that needs special care and I offer, along with the item, to teach you how to care for it
To give off is to emit, as in giving off an odour. Could say the same about giving off an air of (fill in the blank). Giving off an air is to attempt to provide a convincing impression, as in an air of confidence or arrogance or…  One could also start a statement with give on, as in give on the condition of ‘something’. Giving off is not too often received as a gift
To give is to transfer ownership. Like when you give me the keys to your car. In this case it is not forever, but just for some event or such and then I give the keys (the car) back. To give can be to release as in to give a blessing, where there is no payback expected. Unconditional giving is still experienced these days and it has a kind of warm feeling associated with it. I give you this without any strings attached. Wow
To give is also the ability to bend, to allow, as in bending a rule or to give a special consideration. To give is to adapt to the reality of what is. To give is to demonstrate a respect for the person receiving the accommodation. So in this case we are not talking about giving in, in a big way, but in some smaller way. If I give to you and you give to me that can be a trade or it can simply be love in action