To be fair, the MCU kinda doesn't seem to understand how fast non-bullet projectiles go, with Black Widow being able to dodge an RPG round from close range and Flacon being able to outfly missiles from close range as well despite being explicitly not even close to Captain America's physical level and Tony head had tons of fights where he showed nowhere near bullet timing reflexes. And also, to be fair, Diana head no idea of how powerful she actually is, and had spent her entire life training under the assumption that she doesn't want to be hit by projectile weapons.
That being said, Tony was able to at least keep pace with the Winter Soldier for a short exchange when he equipped his gauntlet and was able to out fight Cap himself one he decided to stop jobbing quite so hard and had his computer analyze and counter Cap's fighting style and it's a bit vague as to whether Diana was getting stronger as the movie went on or realizing what her actual limits were, so the bullet wound may still be relevant to end of movie Diana. Still nowhere near fast enough to consider engaging Diana in melee, and even if he does away, probably can't get out of range of her AOE attack, though he may be able to drop some debilitating AOE Sonic attack as she's closing in.
And to address the opening remakes, I really doubt that she'll be especially receptive to Tony's flirting, especially if she knows that there's a blonde veteran named Steve (played by a guy named Chris) from an early 20th century war who flew a suicide mission even though he had a heroic female action girl in love with him still kind of on the market.