Removing brick with the intent of salvaging it is a BIG PIA. You have to do every bit by hand, with a hammer and brick chisel or small air chisel if you have a compressor. You can't just sledgehammer or breaker hammer the wall down as would be the usual. Cleaning that brick for reuse is an even bigger PIA. All of the mortar has to be cleaned off in order to be able to be reused. This isn't something you'd want to hire out as it's extremely labor intensive, and labor is a lot more expensive than just sourcing your brick new and ordering a couple of pallets.

You'll have to build a foundation for the "link", and decide on how you want to integrate the roofline, pay a good mason to make it look "seamless", etc. The expense of doing what you want is liable to greatly outstrip any utility gained by linking the two structures. Also, linking the two structures will affect how your property taxes and insurance rates are calculated, as the garage will no longer be considered an "outbuilding" but will be considered square footage of your primary residence.