Right **** face:
Always contact the local council, it is only a phone call and some sketches and can save you a LOT of hassle in the end...and be costly.
Have a word with the neighbours and tell em what you intend to do. It is governed by the party wall clause even tho it is only a garage and you need their consent to do any works which will involve that middle wall. If ya not going to touch that wall AT ALL then you dont need their consent but be polite and tell them anyways...
Personally id knock the lot down as ive seen pictures and start again

Would. Nice new garage base(raft) and built of that,,,,no need to dig deep founds for a garage. 6 inch thick concrete base, thickened up to 9 inches around the edges where the BWK sits.
If you are extending then dig founds, if it is clay then you should go down a metre as clay expands and contracts with dry and wet conditions. Anything else then go down till its solid, but no less than 500mm. Fill with concrete to about 225mm below finished floor height. Then start the brickwork. As pon said, get a book on how to lay Bricks its easier then telling you....but basically once you have set out the 'bond' on the first course and laid it in mortar, you then build the corners....about 6 course high for a novice, string a line between both corners on the first course and lay the bricks to the line, move the line up and repeat. Make sure the bricks are half bond and your away...
Its a lot harder than it looks to get nice brickwork and TBH it will look a pig no matter how good at DIY you are...but if its ok for you then
Asbestos: :Lots of controversy over this. MOST household stuff is almost harmless and doesnt need to have professional removal but you do have to wear a mask, get special bags from the environmental waste and take it to the local depot in the bags for them to get rid of.. BUT CHECK WITH COUNCIL FIRST!
Any things else just ask....