It was...embarrassing.

The first time he wielded a greataxe, a real weapon, was on his 14th birthday. Despite protestations from his mother, he had joined the Marauder's Guild. At this point in his life, he was already deeply resentful of his own weakness, yet no amount of martial training seemed to make him a worthy Warrior.

He remembers constantly losing his balance, struggling to maintain his stance under the weight of his weapon, barely being able to swing the head with enough force...

All that changed when his Inner Beast awoke.

He would probably try to investigate the imposter's last known contacts to determine where he might be (easier said than done, he may have to call on a couple brainy friends to help). Once cornered, he'd probably attempt to apprehend them and either turn them into the authorities, or...if they've REALLY abused his reputation for nefarious ends, probably kill them where they stand before they have the chance to do anymore harm, then check his belongings for clues to attempt to fix whatever the imposter's done.

Not much of one.

If he's on the road, he will likely look for appropriate shelter, start a fireplace if needed, and meditate.

If he's staying at an inn, he'll take a hot bath/shower if one is available and have a decent meal before heading to sleep.

It'd very likely depend on location, aetheryte access, and the interests of the date. With his inexperience, he'd be more likely to go with whatever they suggested if they had an idea. If he had to pick...

In Eorzea, it'd probably be dinner at the Bismarck, a night at the Gold Saucer, or maybe a show at the Amphitheater.

In Ishgard, it'd probably be just some sightseeing. The city is full of vistas for long walks.

In Thavnair, they'd probably either go shopping in Radz-at-Han's bazaar or go sightseeing out in the wild proper. He was taken by Thavnair's natural beauty when he first arrived after all.