1. Set Program Updates to Manual - That said I haven't been nagged about updates on my XP Pro system, but it is a month or so since I last used it. The download links in that first post are for an XP specific installation, so it shouldn't offer an update beyond version 18.8
They already are, yet when it thrashes my drive and I run Process Monitor, I see entries go by (I can't think of any specifics at the moment) that give the impression that it's trying to download/install an update. It wouldn't be the first time that Avast (and other software) has tried to download and install an update against my will.
2. Yes you still need to register, you're using the program and you are still getting VPS Update support.
I never really understood the logic of making people register a program they're not paying for. Doubly so now that they don't even intend to support older systems.
3. I experienced some CPU spikes (but not on the regular basis you mention) that certainly isn't the usual behaviour, as a resident AV it is only scanning active files, etc. However there hasn't been any update this now 'unsupported' OS version. I would suggest reverting to default avast settings and see if that helps. You might notice from my signature below posts that I'm using avast free 18.5.xxxx check through some of my posts in this topic and you can see why.
Is there a place to download older Avast versions? The last time I downloaded an installer, was in the 7.xx range. I always used Avast's built in update to install new versions. In the past I would have gone to FileHippo, but it appears that they no longer offer downloads of old versions, just a link to download the latest one.

Somewhere along the line, the built-in updater apparently screwed up. I downloaded a file that Avast's local scan showed as clean, but it turned out to be malware (luckily not a virus), When I uploaded it to VirusTotal, their version of Avast flagged it as potentially harmful. Supposedly my version of Avast was up to date, but it still told me that the file was clean.
Then there's the disk thrashing. I'll be doing something, the C drive will start making noise, I run Process Monitor and sure enough, it's Avast. 99% of the time if something is thrashing my C drive, it's Avast, and it seems to do this at least once per hour. I see lots of references to Setup in the Avast directory. Each time this happens, I seem to lose about 200-300 of hard drive space, although I'll be damned if I can figure out where it goes since the times I check Avast's directory before and after, there's never that big of a change. That said, Avast is currently taking up over 1GB of space.
Then there are the times I'll walk away for a few minutes, come back to find something thrashing the C drive and Process Monitor tells me that AvastSVC is performing a "QueryOpen" on what looks like every single file on the drive. It looks like it goes through everything in Program Files, everything in my Work directory, etc.
To be honest, I haven't been that thrilled with Avast for quite a while, I just don't know what would be better to replace it with. I hate that with every new version, they seem to add at least one new EXE that needs access to the internet. I hate that they removed the status window when doing a manual scan. I hate the way the "emergency" updater runs every single day like clockwork, even on a fresh installation. And I really hate the way they bundle Google's crap in the installer and try to trick you into installing it by pre-checking the boxes and making them tiny down in the corner of the window. I once accidentally neglected to uncheck them and while my firewall blocked the installer from downloading Chrome, it still managed to install Google's updater, which does
NOT delete itself automatically if there's no Google software installed despite what Google claims. I know this because I discovered it running on my system a month later. Since there's no uninstaller for this crap, I manually deleted it, although I never was able to remove 100% of the s*** that it put in the registry.