Falling...
Although Spider-man is stronger than a normal man, his muscles and ligaments would not survive a sudden catch when falling unless the web is slightly elastic.
When any object is moving it has momentum, the faster it goes and the bigger
it is the more momentum it has. To stop an object it takes a force acting
over a period of time. The longer the time you have to stop an object
the less force you need.
Mass x Velocity = Force x Time.
If Spider-man’s web is not elastic it will be a very abrupt stop (short time), which means a massive force acting on him to stop his fall.
If his web is elastic that allows more time to pass as he slows his fall, this reduces the force.
Swinging...
Swinging faster…When swinging through the air Spider-man can only ever swing to a lower height than he starts from.
During a swing Spider-man starts with gravitational potential energy (GPE), this is transformed into kinetic energy (KE) as he swings down, then back to gravitational potential energy as he swings back up. He will also lose some energy due to air resistance.
But he can’t gain more GPE than he started with and so can’t swing higher.
The only way he can gain a little more height is to swing his legs at the right moment during the swing, but this will only add a little more energy and work once per swing.