Imagine a spider as big as an African elephant weighting 1 metric tons or less loves to leap from buildings to buildings, I wonder would it legs still works like it used to for the tiny critters using Van der Waals force or shoot its webbing everywhere and swings around like spiderman? Building structures may include concrete walls, steels panels, glass windows & aluminium facades.
If you're asking for hard science, then pretty much everything you stated is limited by the the square cubed law which states that surface area increases by the squared while volume increases by the cubed. Muscle increases in strength by the area (squared) while weight increases by the volume (cubed) so weight increases faster than strength does. This also affects the width of the legs and feet required to support the body weight, as well as the pressure exerted on an animal's body when it falls and hits the ground (as well as air resistance's ability to retard a fall).
Consider that an elephant is heavy enough that just falling from a couple of feet could be fatal, let alone leaping from building to building.
Whereas a flea has the muscle power to leap many times its body length, when you're lucky to be able to leap half. A flea can also fall from nearly infinite height and be fine due to air resistance. Even if there was no air resistance, the flea could fall from a much higher height and survive the impact than an elephant.
I would think that the Van der Waals forces would also hit a square cubed law limit, although it does work for things as big as geckos which are pretty big. I don't know where the size limit is but I bet it is probably long before you get to the weight of an African elephant. The only way around this I can think of is to make the animal get lower and flatter, with wider and wider feet as it gets larger but then you end up with something that is like a flattened slug.
Also, spiders use a hydraulic system for their muscles and that doesn't scale up either, as do many other aspects of their physiology such as their breathing.
Silk would still work though.
Or you could just ignore all that pesky hard science stuff in your story.