Let's see some examples. "I shall go with you." "I would go with you if I could, but I can't because I already have another appointment." "If I were you, I would go hiking tomorrow as your leg is injured, but this is just my advice because in fact I am not you and shall never be you. I myself shall definitely be going as I love hiking." So you see, if you say "I would", it doesn't mean you will do it or even intend to do it yourself. If you say "I shall" it means you will do it or at least intend to. That's a big difference, isn't it?

Would can be either conditional or subjunctive, but it is often used (as your examples demonstrate) interchangeably with will. Will is an inquiry after the consent of the respondent, whose inclinations comprise the sole issue at hand. "Will you give me some advice?" literally means it is up to "your" discretion either to give or withhold the advice. "Would you give me some advice?" on the other hand implies some other conditions may affect your decision. Unstated but implied in this sentence may be some other information. Or there may be a contextual linkage or even a direct statement. I think of Dr. Seuss's Green Eggs and Ham:

'Will' is used to say what we believe will happen. 'Would' is used to talk about hypotheses – things that are imagined rather than true.

Would can be either conditional or subjunctive, but it is often used (as your examples demonstrate) interchangeably with will. Will is an inquiry after the consent of the respondent, whose inclinations comprise the sole issue at hand. "Will you give me some advice?" literally means it is up to "your" discretion either to give or withhold the advice. "Would you give me some advice?" on the other hand implies some other conditions may affect your decision. Unstated but implied in this sentence may be some other information. Or there may be a contextual linkage or even a direct statement. I think of Dr. Seuss's Green Eggs and Ham: