You most likely don't need to change anything about the bike.
If it's got really forwards bars, I'd recommend pulling them back a bit (I found the goldilocks zone to be TT High Rise bars with the "rise" perpendicular to the floor, but that'll likely be for my tastes, on my frame/stem combo, so take that with an armful of salt), and do yourself a favour by keeping the chain nicely tensioned.
Other than that, your balance point is always a bit more extreme than you expect. On the back wheel, you need to sit a bit further back than if you have a brake. On the front, you need to be a bit further forwards.
Be prepared to spend quite a while back in the "fundamentals stage" before progressing again. It's weird because you know you can ride, and you know you can do certain things, but you have to do them all just slightly differently.
I would advise:
Learn to gap to 90 in both directions. I didn't, and it constantly limits my line choices.
Spend a lot of time getting the feel of pedal pressure. Just face up a slope and try and stay on the back wheel without hopping. Squeeze the drive gently to move forwards a bit and let it roll back if you need. Waggling your knees can take care of a lot of balance issues. Obviously hops are pretty much essential sometimes, but they can be far less predictable than just correcting your centre of gravity if you can.
Not necessarily, but I found everything improved with firmer tyres. I like the direct feeling. This is personal preference, with the exception of larger gap to 90s. With low pressures the tyre can tear off the rim. Knowing where you are is very beneficial, so removing squidge can help with that.
Without wanting to sound too touchy-feely, brakeless is far more intimate than riding with brakes. I think that's part of why firm tyres feel better - the bike really starts to feel like an extra limb, and having soft balloon tyres makes it feel like riding with big squishy gloves on. You can never really tell what's going on, and when the lump you're using as a stopper might only be the crack between two slabs on the floor it's really useful to have that feedback.
Ask anything specific, should you have questions.
But be sure to quote or PM me so I get a notification. I'm not here so much any more so will probably miss standalone comments.