(1) when you do some thing and at the same time if something else is also happening then you can use while."I HAVE BEEN PLAYING GAME WHILE WAITING IN QUE-outside the bank.

(2)He,as well as his uncle ,is coming next week. Be carefull while using verb (SINGULAR).

(3) Rather is same like prefer,but former is followed by base verb. I would rather go out than wait for him.
If you say the same thing by using prefer,it would be like; I would prefer to go out than to wait for him.(to + verb).
(4) Whether is used to introduce alternates, like; It is not your matter whether i stay or not.
For could,would,might, should, google model auxilary verb and their usage.
(5) Let means to allow; i will not let you do this again and again.
I hope this would be helpfull.

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SHAH