Will I be able to install FCP10 & Motion on a MacBook Pro with M2?

You will need to check if you can get the latest compatible version as a free download since yours is quite old. Here is some general info you might want to check out:

Copy a Final Cut Pro project to another Mac - Apple Support

https://www.motionvfx.com/faq-motion-5-fcp/answer/apple-silicon.html

My older version of Motion no longer works in Monterey and FCP won't either. I can get a current version, but am being asked to pay for it. So I maintain a bootable OS on an external drive that will allow me to run both as it is no longer worth it to me to spend up to $1,000 on that software again.

You should be able to simply download them from the App Store and you will automatically get the Apple Silicon version. 😉