Just got a hardtail and I am getting it ready for the road. Sidewall PSI range goes from 40-65 PSI but at 20 PSI, it carries me with no tire deformation and feels solid. Do those sidewall ratings are a set rule or can I use less PSI according to my riding? For now, it would be hard surface riding. It is an inner tube tire.

Another issue would be some minor rubbing on the front rotor from the adjustment cylinder. If I loosen it, it will loose braking. Reading some forums, most people mention to ride it and it is part of the break-in process. I am planning to re-center the caliper if it doesn't go away after the first few miles.

Any recommendations?

Really depends on your weight and surface you ride on.
We have really rough roads here so I tend to run pressures a little higher.
Trying to avoid pinch flats and adjust for comfort is just trial and error.

What do you weigh?
20psi is pretty low for a typical 2.25-2.5 MTB tire, but if you're not getting any deformation, squirming, or pinch flats maybe it's ok for you?

For comparison, I'm 210#, and typically run 30 in a 2.4" tire.  With a 2.6 I'll go down to 28, 3.0", maybe 25ish psi. 4-5" fat tires 7-10psi.

For road I max them out.

Unless I was in sand, I’d never go lower than 35-38. Basically what my tire guy quoted to me.

I'll try to hit all your concerns.
20psi is to low for tires regardless of deformation if your an average or Larger man. The one thing I did not see was whether you are tubed or tubeless. With tubes running low pressure will give you pinch flats. You need the pressure to be high enough to prevent that so say at least ~30psi give our take. Tubeless I run 24-26 on dirt or sand depending on conditions and trail. Road you would want some higher pressure for less rolling resistance. Your issue with the brakes would be that the rotors are not set quite right and centered. Adjust the pads back all the way so there is no contact and then center your rotors. Once they are centered then you can adjust the reach and pad location.

Go online and google a couple of the tire pressure charts. Big difference between tube and tubeless, dirt and pavement.
For me I’m running 15 front and 20 rear on the mountain bike. 50 front and 58 rear on the road bike.
Both are tubeless.
The gravel bike splits the difference

Mountain bike or hybrid?
Do you have a smooth strip in the center of your tire?
If I was airing someone else’s tire I would probably call it good at 50psi

for me.

4.4" 8psi, 5 in snow.

2.6" 18/20

2.4" 22.

Front: 2.5" tire: 23 psi, tubeless
Back: 2.3" tire: 29 psi, tubeless

Current riding weight: 225 lbs

The larger the tire, the lower your psi can be to support a given mass of rider and bike.  Big guys like me tend to run 28mm tires on our road bikes so we don't have to run 23mm tires at 120psi and rattle out filling out

Most tire mfg have charts on their websites with a weight vs tire pressure curve.  Start there, and go down in small incraments until you start having pinch flats(snake bites )

Hi there!  

Boy Scout merit badge counselor here.  I teach the Cycling merit badge - but ONLY the mountain bike version.

Right off the bat, I have EVERY Scout LOWER their PSi to 30 PSI.

Never had an issue.

They probably only weigh 100lbs
Every time I lower my pressures I get flats. I also stay around 35psi.
It really depends on tire and size riders weight.
It's super rocky around here on several of the trails so I end up getting rim strikes and flats