Desire Reboots random when playing game or text message.

TBH I can't make much of these logs, but if the last crash indeed had to do with the facebook pics loading, I'd look in the direction of the facebook app/syncronization. 
It might explain the random freezes/reboots too.  Perhaps they coincide with the phone trying to sync the facebook account.  But that's just a guess based on the info you gave.

As for HTC's answer, I received the exact same one a while ago when I had random reboots on one of my phones.  You can pretty much ignore that phone number, as they seem unable to tell the difference between Flanders and the Netherlands.  As soon as you select dutch, they automatically give that dutch number instead of the belgian one.
IF you need to get it repaired, there's no point in contacting HTC to "book it in" anyway.  Simply taking the phone back to the shop should suffice.

Sam, it's definitely a random reboot. Best option is to get a warranty repair. If you are headed to the official HTC shop, demand a mobo change.

Bombard their email with demands for a mobo change. For real.

owkay, I went to the store to pick up the phone. I received a nice white box with a patch on it (fixed). Inside I found my phone with some documents that the imei has been changed.
So now I'm installing everything back and but the settings back so I can start using this wonderful piece of art.
That was what I thought when opening the box.
But I do have one question left: If, I hope it never happen again, but if I have to take my phone in to service for repair, is there a HTC Servicecenter or something in Belgium?

I read some post on different forums about HTC's going to Euro-Twice, mine went to Dynafix. First I had some doubts about that company but for now I didn't had a single problem with my Desire. (Fingers crossed, the problem started after 14 days)
So I hope I don't have to get it back in to service soon. But I still wonder what triggers the reboot error. Since I got this problem I only read (search) postings about this rebooting.
Is there anything I (end-users) can do or not do to avoid the phone doing this? I know that bad software can mess up some hardware, so maybe it happens because of installing something...
I can honestly say that I take lots of care for my phone (and everything else). I don't drop it, shake it badly, use it in the bathroom or outside when it's raining or foggy...

Except for the issue I had, which is still something that keeps me awake, and the keyboard that I can't seem to get use to, I recommend this piece to everybody who want's to buy a 'smart'phone.