In the first camp, where you have to jump from the two wood swings to the net, every time I jump to the net I fall. I'm using the PC version. I've tried jumping different ways and pressing F while in air but nothing works.

Really not sure whats wrong with that, but if you are using a kb and mouse, I'd recommend that you get a gamepad. The demo version was a bit hard for me. Jumping and hanging was pretty frustrating on PC without the gamepad.

I can jump no problem. I bump into the tree but then just keep falling rather than latch on the net

Im not really sure, i automatically latched onto the net that was on the tree. Not sure why you keep bouncing off.

I used the mouse and keyboard with no problem. I have a gampad pro and I was going to use it, but I liked the mouse and keyboard better because I could change the camera view easily and all the actions were accessible(gamepad pro has like...9 buttons and the game has more actions than that). Maybe it's your keyboard or mouse...maybe the typematic rate needs to changed in the bios...maybe the timing was wrong. I dunno. Sometimes it's just a matter of familiarity with the peripherals.

or a change of settings. I couldn't play with keyboard and mouse until I inverted the mouse axis(one or both, I don't remember) and change some of the buttons around.

While I own a pretty good gamepad I never felt compelled to use it on the demo. I think the mouse/keyboard controls work nicely.

Did you try to hit the net at different heights? Maybe you had too much momentum and hit too high?

Ok I finally figured it out. For some reason I had to take my finder of the forward key and hit it again to stick.

But....now I'm stuck somewhere else and want to make sure it's not something similar:

When I get to the top of the wall with the metal swing poles interspersed with the fire jets, I don't know what to do. I try and jump to the netting on the left, but I keep falling. When I jump on the rock to the left and jump to a few more it doesn't seem to get me anywhere. Is this another case of having to time the jump to the net correctly? Thanks.

I'd have to look at it again. There are two like that, right? If you can find a screenshot, I can tell you.

I think there might have been two. If so, this was the top one. At the top there is a big wall in front of you and there is no place to go but off the ledges to the right or left. On the left, the wall continues a bit
off the ledge and higher up there is what appears to be some climb netting. There are also small rocks to jump on but I think they are so if you screw up the net jump, there is a chance to climb back up to try again.

If you are where I think you are you have to punch the wall in front of the net. It should have a crack in it already I think. Just punch once and go on through. :)