Is the following English message correct grammatically and polite?

[Mircat]

You're mixing business with personal stuff and I don't think you should do that. You need to keep them separate.

My message would say this:

Hi Suzy,

Just a note to say thank you for your feedback and comment on my manual. I really appreciate it and I hope the readers will find it useful and helpful.

Regards,
John

It's not necessary or advisable to go into an explanation about how Facebook works or being or not being friends blah blah blah. Go on Facebook later outside of work and message her from there about being friends. You want a simple thank you without being overly wordy etc. You can be wordy outside of work.