Keep in mind I suck at O8b, so take this with a gain of salt.

On the first hand (I hope you were in the big blid), I'd probably bet/call, but not do to much raising unless it's heads up. You're likely looking at a split pot and the last thing you want to do is raise and get heads up with the best low hand on the flop. If his low hits all the two of you are doing is feeding the rake. I want to keep as many people in the hand as possible.

On the 2nd hand, raise as much as possible and hope to push out the flush draws.

fold the first hand, cap the second

Hand 1 is a simple fold. If it was 569 I might play on for 1 bet, not on a 589 flop. You have 1 good card in the deck, a King. if it hits, you have 0 good cards in the deck for the river.

The only way I'm playing this hand is if I think i can get it heads up (or it is heads up) or if I can take it down with a bet.

It depends.

As for the flopped straight, at best you are playing for 1/2 the pot, too many ways to lose the high hand here. Ask any pro Omaha 8 player and they'll tell you "easy fold". Of course, you could always cook up a scenario where you would play it. But, under normal circumstances and nothing else to go on, fold to a bet

Same as folding top set on a 348 board

The problem with your hand is; 2 of the straight cards are above you. You have 0 chance of having the nuts unless 2 unpaired, unsuited cards A-4 fall. and we know that you will only get 1/2 the pot in that situation.

If I'm playing a high hand in Omaha 8 I want to be able to play it fast, not have to sit around waiting to get outdrawn.