1 and 2 are fine

for 3, i think the chances will be affected. Consider 2 cases:

1:- the card we know of is neither 2 or 9

2:- the card we know of is either 2 or 9 (of H or D)

so

P= (top card 2 or 9)*(case 1) + (top card 2 or 9)*(case 2)

or (8/52)*(22/26)+(7/52)*(1/4)

where 22/26 is chances that ~(2,9) was selected from D and H

and 1/4 is chance that either of 2H,9H,2D or 9D was selected.

about 4, no they are not independent because if the H or D is a 2 or 9, the chances of top card being 2 or 9 are affected.

Hope it helps!