Destruction permit required to remove garage
There are many things to consider, even down to what ward you live in and some more you've raised in your additional post.
Depending on your ward (even street or lane-way) you may need to get an additional permit to park in your back, as you suggest. In some locations there is a moratorium on this type of parking, in others it's assessed on a street-by-street, house-by-house situation. If you have a mutual lane-way already, depending on the width, it could be an instant rejection. There are so many factors.
Call a couple of architects familiar with your area, they can give you a better idea of how things work where you are (I only know specifics for Beaches/East York), and can prepare the appropriate permit application and drawings (the city will require a lot survey, full home and garage schematics, etc... with the permit application). It becomes significantly more complicated with the garage connected to the neighbor, you may need two permits (one per property) and your neighbor to agree to his permit submittal just to get the ball rolling...