[JSmith2007]

Hand #1 - I think you may be drawing dead here. Depending on how many players are in the pot, and previous betting actions and reads, it's likely your 5 of hearts is no good anyway, should a river heart hit. Assuming you have the best heart in the hand, you'd have 9 outs. There are 13 hearts in the deck, minus the 4 you need for a flush already seen, gives you 9 more suited hearts to come. Most people will obviously adjust this number because the likelihood NOBODY else had a heart and folded somewhere along the line is unlikely. I'm going to say you've got ~7 outs, maybe drawing dead though.

Hand #2 - Again, you can't just count outs based on hands like this. You need betting action and reads to put your opponents on a hand. Assuming he doesn't have a king here, you don't need to be drawing to anything. You're ahead. If he has a king, you're drawing to 3 aces. Maybe 2 for adjustments.

Hand #3 - Again, betting action and reads. Assuming no king, you're probably ahead and having opponents are drawing/counting outs to you. Assuming he has a king, you're drawing to 6 outs. 3 jacks and 3 8's still left in the deck to make a better hand than a pair of kings.

Hand #4 - This one is a little easier, but still could use betting action and reads. Assuming opponent has a queen, you're drawing to 6 outs again. 3 2's and 3 kings left in the deck. Assuming opponent has a 5, you're drawing dead (0 outs), more or less, get out of this hand before the river hits.