Can I see text messages from iPhone on my Desktop?

Upgrade to Yosemite if your computer meets the requirements.

ugh... I did, and it screwed up my laptop - I had to go back to a clone I luckily had of my pre-upgrade system. After the "upgrade", it would keep the fans running while closed, and all sorts of other behavior I didn't like.

I got as far as signing in to iMessage in Accounts of Messages application (generated a custom password etc.), and it says

"Could not sign in to iMessage: The server encountered an error processing registration. Please try again later."

what does this mean? The console shows

8/19/15 12:27:27.717 PM imagent[307]: [Warning] Empty account query with service: iMessage

8/19/15 12:27:27.775 PM com.apple.SecurityServer[19]: Session 100460 created

when I put in my password and hit OK (it shows my 2 email accounts, but won't let me check them to ON).

That means that there is already something wrong with your system before you upgrade. You should look into how to solve the issues first before you upgrade.

hmmm, what do you recommend? I did Disk Utility, it found no errors. I repaired permissions. I checked the disk with Disk Warrior and Drive Genius - no errors. I upgraded to the latest OS, as per instructions, no errors reported. And then, various issues upon first boot into the new system. I have a late-model Macbook Air which should be perfectly suitable. What to do to solve the "issues"?