Q1.
    (i)  PASS. You need 6+ points to respond to Opener at the 1 level.
    (ii)  PASS. You still need 6+ points. Here you have 5 (inc 1 for doublton) and a 10 loser hand.
    (iii)  Here you have a nice H suit than you can't bid because to bid at the two level you need 10+ pts. Your only option is to bid 1NT. Maybe partner will bid another suit (possibly even H's?!!) which will enable you to show the hearts.
    (iv) You have a fit and 11 TP invite with 3S. 2S is an under bid 4S an overbid.
    (v)  A direct bid to game shows a weak hand with lots of Trumps. Bid something at the two level (PARTNER CANT PASS-can they?) and then show the raise to game. Slow arrival shows strength.
    (vi) Here is the hand that you can compete to the 4 level straight away You have at least a ten card fit and so you can bid 4S. You may even make it!!
    (vii) No fit balanced hand cover in other suits 10 pts - 1NT, with 11 go 2NT and with a good 12+ go 3NT
    (viii) 3NT good hand opp 1S opening.(6 losers)

Q2.
    (i) 2C shows 6-9 pts; 3C shows 10-11, 1NT shows 6-9 pts, 2NT shows 10-11, only leaves 3 NT. Hope like hell partner has stopper in D.
    (ii) 1H  bid 4 card suits up the line. If partner has S he will bid them next.
    (iii) No 4 card major less that 10points Can only bid 1NT. Good luck!
    (iv) 1S = 6+ pts 4+ S You can show your extra length next bid.
    (v) 1D if partner bids S then you are comfortable with NT otherwise re-bid 2D
    (vi)  1S show longest suit 1st can rebid 2 H. This shows 5S and 4H.
    (vi)  1S can show length and strength next bid when you know more about partners hand.
    (viii) 2S a jump bid shows 6 card suit and v.weak hand (3-5 pts). Uses up 2 layers of bidding for the opposition (probably their contract) and tells partner to shut-up. Some people play this as strong (our contract). Not sure why as it uses up two levels of bidding for our side.

Q3.
    (i) (ii) & (iii) 2D In standard american 2D relay is always done over 2C game force opening. Responder will be making the decision as to the contract level and suit after partner describes hand so you do not need to tell partnter your strength.
(iii) Some people play 2H as v.weak. less than 3 pts or 3 J's. 2C opener then chooses contract usually below game - use with caution. No hand has more than 12 losers (at least 1 winner). Partner shouldn't open 2 C with more than 4 losers, therefore should make 10 tricks. His 9 + your 1.