Learn English – “Definitely” vs. “absolutely”

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:

Would you eat them in a box? Would you eat them with a fox?

The terms of the conditional are clearly set forth. The questioner is proffering various inducements to sweeten the deal for the recalcitrant hater of "Sam-I-Am".

In any case, asking either question in conversation will, in the vast majority of cases, be understood simply as a request for advice, without all the grammatical analysis.

In informal speech the word absolutely is often used to add emphasis to a superlative. You could just as easily say, "It was fantastic," as, "It was absolutely fantastic," but both really mean the same thing.

Adding it to words like good doesn't have the same requirement for emphasis, as there is a superlative you could use instead, so you would rather write, "brilliant," than, "absolutely good."