Hey Logician, good to see you over here.
1). Categories, images, and posts are calculated from the totals shown on the category bits above that section (pretty much the same method vB uses on the forum home stats). Then the total views and diskspace are calculated with queries.
2). That depends on which features you have active (stats, new images, random images, etc). With all features active, I belive the query count is around 10.
3). Yes, the RAND() command is used in the query. I know that's not exactly the best method, but I've yet to be able to think of a better one that will easily work in all situations.
4). I'm sure there are some out there, but I'm not aware of one off the top of my head. Here's a few from my personal site though:
index.php - Page generated in 0.59135 seconds with 8 queries, spending 0.0058779716491699 doing MySQL queries and 0.58547202835083 doing PHP things. (Note that's also with 200+ categories all displayed on the main page. If I change the depth option so that only about 5 categories are displayed the load time is down to 0.15287. This is with the stats section active, but no new or random images.)
browseimages.php - Page generated in 0.29186 seconds with 12 queries, spending 0.0074465274810791 doing MySQL queries and 0.28441347251892 doing PHP things.
showimage.php - Page generated in 0.28080 seconds with 10 queries, spending 0.0091509819030762 doing MySQL queries and 0.27164901809692 doing PHP things.
upload.php - Page generated in 0.20745 seconds with 7 queries, spending 0.0089511871337891 doing MySQL queries and 0.19849881286621 doing PHP things.
If you'd like the stats from any other pages just let me know.
- Categories: 1,186, Images: 331,367, Posts: 1,945
6). MySQL fulltext.
7). Instant more like vB2 for posts and such. Subscribed category emails are sent once a day with a cron script.
8). That's a known bug that popped up in the vB 3.5 version. There's a simple fix posted in the bugs forum here. I suppose I should fix that on the demo, but I usually try to leave those files as default.
9). Actually that may be a bug... I have an on going support ticket with another user here who says some of her users are experiencing similar problems, but I've yet to be able to reproduce it or figure out the exact cause. I just tried uploading an image using the same text you posted using IE and FireFox, but they went through fine. Is it only doing that to you when you enter characters like that in the input fields? What browser/OS are you using?
10). Yes. Once a day (assuming there were new images/posts made) an email will be sent to subscribers telling them what new images/posts have been made.
11). No. There are a couple of optional file modifications to group the templates and add the options to the modcp, but even those can be done with the plugin system now (just haven't updated things yet).
12). With the exception of the install file, everything is fully phrased in the vB phrase system.