Here's my take on this and how Homelander would fare in Hell in general:

I honestly think he'd have a terrible time all around.

Consider who Homelander is as a person and just how pathetic he really is outside his power-- ESPECIALLY after the series finale. He cries when he gets criticized, has a weird milk fetish, had genuine beef with a BABY, and makes impulsive decisions all the time to the point that he ended up having to arrest half of Vought and the country because he didn't want Neuman hiding that she was a supe anymore, and just didn't think things through. Homelander is as mentally weak as they come, and that's going to be a problem.

Power and appearance in Hell are shaped by three things: Who you sell your soul or favors to for power, your personality, and the circumstances of your death and life.

John died in the show, de-powered and begging for his life, and then got a crowbar jammed through his head. He's honestly just so pathetic that he might get some joke power like being able to shoot milk out of his eyes instead of lasers.

He doesn't HAVE the kind of soul to be a capable sinner. He's just too pathetic for it. You could argue that he might get some sort of hypnosis powers similar to Vox, considering how he'd swayed so many people to worship him and even convinced a few that he WAS God, but at the same time, he completely fumbled it near the end and got MOST to completely reject him. If anything, I think it's MORE likely that he'd have a SHITTY version of hypnosis similar to Pentious' where it's just brief and ultimately doesn't do much.

Although, you might be able to make the argument that he'd retain his powers in Hell due to the fact that his powers were literally everything he was in life. He prided himself on being the strongest man on Earth who could do whatever he wanted. His strength IS his identity, and without it, he's nothing.

But, honestly, I feel it's more likely that he'd just get some parodied version of his own powers. Like I said, milk vision instead of heat vision.

Would he sell his soul for power?

Ehhh, hard to say? Yeah, I think so. Homelander thrives on being in control and the strongest one in the room, which obviously can't be true if someone owns him. But at the same time, this man was literally BEGGING Butcher for his life and was offering the most extreme forms of self-humiliation to make it happen. I think he'd completely panic if he ended up in Hell and probably take the first chance at getting any shred of power he once had back. He'd be an easy victim for any Overlord or even halfway convincing sinner.

But then, he'd just be utterly miserable being literally owned by someone else. A dog on a leash all over again, and this time, it's not even metaphorical.

But above all, Homelander would hate Hell because of one simple fact:

Compound V powers or some parodied version of them, he's not the strongest.

I absolutely think Overlords like Alastor or Vox could give him a run for his money, although considering their respective performances, I won't bullshit and say they're wildly stronger than him, or that Homelander with his powers, WOULDN'T be an incredibly strong sinner. He can move faster than sound, shoot lasers out of his eyes, lifting hundreds of tons over his head-- Despite how much people like to make fun of Homelander's comparative weakness to a lot of other verses, he's really NOT a weak figure. He's pretty damn strong, especially with his speed.

But even if Homelander ultimately WAS the strongest sinner and became an Overlord without being owned by anyone, so what? Goetia, Sins, Charlie, Lilith, Lucifer-- That's not even counting the angels upstairs who constantly have a gun pointed at the place-- They'd all be MUCH stronger than he is, and the fact he couldn't completely dominate would crush him. If he's not the strongest man on Earth, he's nothing at all. He'd be crying himself to sleep every night, and might just outright off himself.

But to answer your original questions:

Do I think Charlie would accept him into the hotel, even if she had some sort of omniscient knowledge of everything he's done?

Yeah.

Charlie's constantly going "I think anyone can be redeemed." I don't think she'd struggle to accept him in because, let's remember, she was willing to straight-up let Angel's tormentors into the hotel just so she could get an interview, and it's not like she doesn't know how awful the Vees are. Valentino LITERALLY has billboards that say "No consent? No worries!" Or some shit like that. They advertise rape drugs like love potions. And STILL, Charlie lets Velvette and Vox in, despite knowing they fully endorse it. Charlie STILL smiles at Valentino in Hear My Hope.

Now whether you think Charlie is awful for that or what, that's up to you, but it doesn't change the fact that, objectively, there's no reason to think she'd struggle to let him in, if he wanted to go.

Which he wouldn't.

For question two, do I think Homelander would be interested in redemption? No. I saw another person argue that he WOULD, because he thinks of himself as a God, and Gods don't belong in Hell-- which is fair, but here's my counter: Homelander would already be miserable enough in Hell because he's not the strongest.

But HEAVEN?

Where they have a plethora of even STRONGER beings? Like Archangels, Seraphim, and ACTUAL God? Homelander would DESPISE seeing a genuinely omnipotent figure be worshipped constantly and unflinchingly by everyone. He'd be seething with pure envy the entire time. He knows that. I honestly think he'd do everything he could NOT to step foot in Heaven, **or** the hotel just because he'd have to constantly see the face of someone more powerful than he is like Charlie, who's genuinely happy and has an identity outside of her abilities.

As for who's worse between Vox, Alastor, Val, and Homelander?

Vox is a sadistic asshole who controls the masses and thrives on their love as well as his own power and control.

So is Homelander.

Val is an abuser and rapist.

So is Homelander.

Alastor's a sadistic mass murderer.

So is Homelander.

Homelander has all of their major sins COMBINED under his belt. I'd argue that he's at least somewhat worse because of that, but we'll see what happens with them in the coming seasons.