Is there space for a garage in the far back yard or in the front yard? How many trucks and cars?

I think you need a permit for enclosed garage. Get a blue print first.

My advice would be get a architect, and start saving large sums of money.

Doesn't look wide enough. Start with your municipality.

Figure 60-100K for all of the permits, and work needed to do this. But it's doubtful that there is room after you factor in the setbacks.

The only place for a garage is likely to be the rear, with maybe a breezeway attaching it to the home.

With the hip roof, extending the front means reframing the whole roof to work with that idea as either a gable or a different pitch.

This is not doable without some professional design and construction.

IMO there is no room for a garage without encroaching on the next property, you could check about the front porch it seems there is room for that and the comment about egress is valid . IMO the only place you might be able to put a garage would be at the very back of the property where it seems you have a shed now.

Barely sufficient room for a proper car port . The rear yard would be your only option due to your neighbours close proximity .

This advice may seem harsh but given the above comments, take your money and look for a new house with a garage. A new house will be your home just as much as this one is.