Many people have their touchpad that does not work anymore or badly after updating to elementary OS Hera 5.1
The solution has trouble, as you can see in the discussion is to update the Kernel. Can you confirm that this is the same for your computer model?
$ sudo apt install --install-recommends linux-generic-hwe-18.04 xserver-xorg-...
I see you do not have the new Kernel tried to update it
$ sudo apt install --install-recommends linux-generic-hwe-18.04 xserver-xorg-hwe-18.04
I think that will solve your problem, someone else also had this problem here
Old answer but for the second question :
Nice to know you started linux. I wanted to exploit as much as possible the Touchpad of my Dell XPS 13 laptop with multi-finger motion function.
So here is a tool that I use now with my laptop daily
Having automated this task for the installation of Elementary OS on ...
Apparently he would have to update the kernel, I answered someone a few minutes ago on another post.
Launch the terminal whithout mouse and shortcut for terminal
SUPER + Space
Search terminal or the name of your terminal
Follow instruction in the link to the top
I used to have the same problem with this laptop (not a huge fan of touchpad anyway), so much so that I ended buying a mouse.
But recently I discovered that if I touch the pad very very lightly with two fingers (before the two fingers-touch had not worked either) BUT delay a tiny bit longer than a regular left click, when I release the pad the right click ...