It sounds like you have trusses, thus the "lots of supporting wood beams across."

The ceiling will NOT hold your weight (it is likely 1/2 inch drywall).

You need to keep your feet on the lower truss cord, and even then you may create some drywall cracks depending on how heavy you are.

If it is hard to get around in the attic, just cut a hole adjacent to the register large enough to at least get your head in to look around.

It is not that hard to fix drywall.

If you have a closet on the 2nd floor, hire a handyman to make you an access. Out here they are required. Tracing leaks can be as simple as tracking water stains or as involved as having someone water down areas of the roof to try and spot seeping while in the attic. If you dont feel confident about being up there in the attic, a reputable handyman can help you out. Ask around for referalls to find someone decent.

Thanks for all your valuable comments. Could you please offer
me further suggestions?
The water leak dried off the ceiling but I still see water leak of darker color on side wall near the corner.
Does this mean that the panels of wall and ceiling should also be replaced in addition to finding and fixing the water leak above it?
Also, when I fix it (or had it fixed by handyman), how should I block the water dripping from my neighbor side to my side? Some sealant would suffice or should I put some extra structure put on?
Many thanks again!

It sounds like the neighbors "roof windows", I'm assuming skylights, weren't flashed properly. It is your neighbors responsibility to fix the leaks if you find that is where the problem lies. Get together with your neighbor on this. Concerning replacing wall/ ceiling panels, probably didn't get wet enough to cause damage enough to replace but will more than likely stain. A good stain blocker/primer after it has dried well followed by two coats matching paint.

Stained drywall may need replacement, or at least a stain killing primer and a fresh coat of paint.

If your neighbor is allowing water to enter it is HIS problem to fix, not yours.

Since you are new to our country, my thought is to ask you about the type of ownership you have. If you truly own the town home from your curb to the back of the lot, the advice you have gotten above works fine.

However, if the unit is a condominium or co-operative, things are handled differently. In that case, you probably do not fix a roof problem yourself, you would report it to the condo board or manager, or someone like that because in a condo, you only own what is inside your walls, not the structure itself. A cooperative is likely more complicated than a condo.

Hi!

You may need replacements on the drywall so I suggest that you get a handy man or roofer to do this job.

Here is a link that might be useful: Calgary roofing