I do not know the answers to your specific questions because I am not an expert on how TimThumb works.
There isn’t anything new or different I can tell you about this issue. That’s the truth. Whatever questions you have about this issue, if you can’t find the answer by searching this forum for “400 bad request” then there will be no point in asking me because the answer will be “If you search the forum for ’400 bad request’ you will find everything I know about this issue. There isn’t anything new or different I can tell you about this issue.”
Ultimately this is a server issue and you can maybe save yourself a lot of frustration by asking your web hosts to fix the problem with their server that isn’t allowing the TimThumb script to work properly.
I can’t fix the problem for you, and the only advice I have on this issue has been posted in this forum multiple times.
There really is not anything new or different I can tell you about this issue.