Learn English – Corresponding or associated? Which to use

In general, aim, goal, objective can be considered synonyms, but consider these Google Books results:

long-term aim 197,000; short-term aim 32,500
long-term goal 255,000; short-term goal 471,000
long-term objective 115,000; short-term objective 161,000

I think what that tells us is that aims tend to be more general, vague, non-specific, long-term, compared to goals, which are more likely to be specific, short-term targets (objectives are somewhere in between, or more accurately, they simply have no relationship with this distinction).

Thus, you're more likely to have a long-term strategic aim/objective which is broken down into component goals in pursuit of that aim, rather than a goal which is achieved by meeting several subsidiary aims. But this distinction is nowhere near a "rule", and few would see anything odd in reversing the usages.

In the context of a resume or curriculum vitae, I'd probably use objective, if for no other reason than it sounds a bit more formal/professional.

EDIT: Regarding the point about goals being more associated with short-term aims, I think it's worth pointing out that a goal in ball/puck game contexts (soccer, say) is just one step towards the aim / objective (to win the game). A bit like Winning the battle not the war.

Yes. You could say either:

I couldn't handle this situation without your help.

or:

I couldn't handle this situation with no help.

In the second sentence, you could say "without help" or "with no help" interchangeably. "Without help" seems slightly more correct to me because "couldn't...with no" seems like a confusing number of negatives for one sentence. However I think that's just my personal preference; it is probably technically correct either way.

In the first sentence, with the article "your", you can only use "without".