Are there exercises you can do to improve accuracy without actually shooting the gun?

If the gun is a rimfire, buy snap caps and practise with them. Rimfire snap caps are small plastic bullet sized things that sit in the chamber and you can droo the firing pin down on them safely without doing any damage to the gun.

If the gun is a centerfire, you can dry fire it (shooting it without ammo) but do not do it excessively without buying snap caps of the appropriate caliber.

There are snap caps for center fire rounds, I have some for my 308 win.

Practice with them in your firearm. Being familiar with your fire arm is important.

Practice "shooting" and getting into-and-out-of the four basic shooting positions, prone, sitting, kneeling, off hand. Lastly, visualize the whole process from spotting the target, getting into shooting position and squeezing off a "shot" through the target getting hit. Along with BRASS, breath, relax, aim, sight, and Squeeze.

Dry fire practice. As CTM has rightly pointed out, if your pistol is a RIMFIRE, DO NOT DRY FIRE. (Rimfire = .22 LR). If your pistol is a CENTERFIRE (Centerfire = .25acp), dry fire to your heart's content.

The reason why you do not want to dry fire a .22 (Rimfire) is because the firing pin, without a rim to crush, slams against the steel of the rear of the firing chamber. Eventually, this will cause the firing pin to break.

A centerfire pistol does not have this issue.

Only using a BB gun or pulling the trigger without bullets in it

If your Beretta is a 22LR DO NOT DRY FIRE IT. If it's the 25ACP version dry fire to your hearts content.

depends on your gun, but dry firing helps with flinching and trigger finger control.

Heck yes.

There are weight exercises you can do to strengthen your arm. You can buy a finger exerciser to increase the power of your grip. Like this:

http://www.amazon.com/Gripmaster-MEDICAL-Exerciser...

and like this

http://www.amazon.com/Finger-Forearm-Resistance-Ex...

You can buy an affordable pump pellet pistol and use one of those for overall practice of breathing, holding steady etc.

I - am not a fan of dry firing. Never have been. Even guns that are listed as safe to dry fire.....the ones people have been doing this to for years end up showing damage of some kind.