I'm looking to buy a new wireless mouse.
1) Regarding the ones that have buttons on the side, is it easy to accidentally press those buttons while regularly using the mouse which requires having fingers on the side near them?
I have had a number of Logitech mice (both wired and wireless...currently using a wireless with six side buttons) with side buttons and never had any issue with accidentally pressing those side buttons. For all such mice that I have used, the design is such that there is a natural place to place the thumb that is below the buttons. So, you actively have the raise your thumb up to press one of the buttons.
But, I suppose it would depend on the design. As I said, all the mice I have used with side buttons have had a natural place for the thumb to rest. While most mice with side buttons that I have seen have very similar designs to the Logitech mice I have used, it is possible that there are different designs that might make it slightly easier to accidentally press a side button. But even then, you still need your thumb to be "flailing" around with a decent amount of force as most side buttons require more force to push then your typical left or right click button.
2) Are there any companies whose wireless mice are still vulnerable to Mousejack? And are there companies that are known for not being vulnerable to it? (Like maybe TeckNet?)
I do not know of a definitive and exhaustive list of which mice are or are not vulnerable to it. The best list there is out there is this one:https://www.bastille.net/affected-devices
This list only contains mice that they tested and where show to be vulnerable. They have a "disclaimer" at the bottom of the second table that basically says they could not buy and test every possible mouse out on the market, so the list is not definitive and exhaustive...i.e. there might be other vulnerable mice out there.
From what I understand, typically the higher end mice from companies like Logitech did have encryption. It was mainly lower end mice that were vulnerable. I would expect that many mice manufacturer's newer mice (i.e. designed and first released since the discovery of Mousejack) likely are designed to not have the vulnerability.
As I understand it, the best thing to look for is that the mouse is used AES encryption. And FWIW, I could find no indication on whether TeckNet mice did or did not use AES encryption, so I have no idea if they are vulnerable or not.