It's not possible to answer the question as asked. There are too many types, models and variations of these guns to consider. These guns can sell for as little as a few hundred dollars and up, depending on what it is, when it was made and condition. Condition is everything when appraising a gun. As always, it's recommended that you have it appraised at a Gun Shop or qualified professional.
.32 Auto IS .32 ACP (Automatic Colt Pistol). It's also known as 7.65x17SR, 7.65x17 Browning, and 7.65x17 Browning SR.
100-500 USD
The 32 ACP or 32 Auto is known as 7.65 Browning in Europe.
it should say right there on the receiver "made in Belgium"
Not necessarily. There are a number of rounds marketed as .32 Caliber or 7.65. .32 Automatic Colt Pistol, .32 Auto, 7.65x17SR, 7.65 Browning, and 7.65 Browning SR refer to the same cartridge. They are not compatible with other .32/7.65mm cartridges such as the .32 Long Colt, .32 NAA, and others.
Not in Belgium barrels
The 7.65 automatic pistol cartridge is also commonly known as the .32 ACP, or for short, .32 Auto. Any browning pistol chambered for .32 ACP uses 7.65.
You let a trained gunsmith fix it.
10-1000 USD depending on specifics
I would need to know the Browning model number besides the serial number to get you any info on your semi-auto browning pistol.
50-500 depending on specifics
100-1000 USD