The hand looks pretty I would not be 3 betting it pre with the 99 in the hand - this is not to say you shouldn't sometimes. The pair blocks your outs and reduces the value of the hand.

As played I would be betting this flop although you need to be aware that to a check raise pot you are lucky to be into just 2 pair and the T8 gutshot. If he rolls any kind of AQT with hearts your equity is reasonably bad and hands like this should form a reasonable percent of his early opening range. Any pair + higher flushdraw and you are in bad shape. You can bet here though to pressure and fold a lot of hands that are ahead of you currently or that have reasonable equity against your straight draw and flush draw. What you do to a check raise is villain dependent.

This is one of the harder aspects of PLO as UTG is check potting sets, 2 pair, and better draws.

Preflop I agree with Josh. On the flop I would check back if I saw before a lot of check raising from my opponent otherwise bet/3bet is fine.

Flat pre is better when he is short. Its not really a hand that is ahead of his opening range so just try to see the flop as cheap as possible.
With 2 SPR and the betting lead there is nothing to do but get it in. If we where deep say 5 SPR or more we can check back and take our equity.