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Yes

Currently it's determined by installation order.

This sounds like a very old problem that was fixed a while ago with conversions.
Try seeing if the group ID for user ID 1 (the guest user) is set incorrectly.

Enable debug mode, paste the full errro

You want to change all of the forum permissions to category permissions? If so, you'll need to rewrite all of the queries that reference the forum_perms table (and admin_forums.php).

Yes, by editing viewforum.php to have the query only return topics with last post times in the last x days. You would also want to add an index to the topics table on that column.

And again, that doesn't make sense. I don't know about the whole "nonstandard" thing, I know MySQL and SQLite do it. However, it doesn't address the issue of how to escape a character if there are no longer escape sequences. For example:
foo="this is a string"
lets say that string is created by user input. Without an escape character, how do I prevent this?
foo="this is a string" or 1=1 or foo=""

That's probably correct

That is what happens for normal users in general, I believe.

Yes. Disable registration and use the User Management plugin to manually create accounts.

As Vovochka said, if extension authors want to use variables for storage, they can create variables with their own names based on extension ID. There will be developer documentation at some point that explains more of these kinds of things. Essentially, there is no way to keep extension authors from stepping on each others toes deliberately. The method we use here for extensions is good in that it gives access to variables that you can't necessarily get otherwise (eg: a hook like what we have in a function lets you globalize a variable and use it: other systems would have to resort to using $_GLOBALS because of scope issues). On the other hand, it also means that your code is executed like regular code, which means it can overwrite variables unintentionally if you don't follow naming standards, etc. No different than a modification.
In the words of Spiderman: "With great power comes great responsibility."