Is there something similar to the puppet tool from AE in Hitfilm because I haven’t found anything. Could I use the quad warp?
No, there's no equivalent to the puppet tool, though it would be very useful. You can use the quad warp for a few things, but only as long as they're quite simple, otherwise you'd need multiple instances of quad warp and it would quickly get really messy. Have a try at how far you can go with it, though!
If you're trying to warp something like an actor, you CAN use mocha to generate some roto masks, create a point rig for joints and layer things together to do 2D puppet animation. It's a bit tedious and certainly a lot harder than using the Puppet Warp tool, but it CAN be done.
Do you have to have a certain version of Mocha or not?
Mocha Hitfilm 4 (bundled with Hitfilm 3Pro) will be fine.
The puppet tool would make a nice addition to the next update of HF 3, don't you think :-)
It would, but I think we're more likely to get that in HF 4.
We also need a roto brush tool.
The bezier warp can probably do what you want the puppet tool to do, just a bit less control. I'd say give it a try. Still, a puppet tool would be quite useful.