Two Bugs and some comments
 

I have found that sometimes when I opened new connections and I try to put a 0 in to the connections box, the program will put a 3 instead and present a warning message. Also the force resume buttom will not requeue a file unless there is one downloading already, even if I know that the file is available and slots are open, the program will sit with the file until the time runs out. Also, regarding the times, they are way too long. 10000s? what! The timeout for downloading files is too long as well. Sometimes, a file will sit a 0 kb/s for hours, and I have to deleted the file. Force resume should be able to requeue such files.

I cannot confirm that bug. Which version are you using?

LimeWire is probably waiting between to requeries. Forcing to resume won't have any effect except for some rare cases, when there is an error.

Try restarting limewire instead, so the incomplete file won't be lost.

The default requery interval (for every requery after the third) is set to 3 hours for a reason, by the way. Every requery creates a lot of search traffic, while only a few new hosts are found. This search traffic however forces the Ultrapeers, who can't necessarily handle all of that traffic to keep up less connections (as for to cope with the traffic) which reduces your search horizon and the number of search results you receive. So if you requery more often (some clients like the infamous Xolox did so) you are reducing the number of results for yourself and for all others sharing the network.

I am using the latest version 2.3. The problem with the connection box changing an inputed 0 into a 3 only happens sporadically, but it is kind of annoying.

Then don't input 0.
Click on File->Disconnect in the menu instead, since this will work for sure.

Ah, and what also might have happened is, that you accidently entered the 0 behind another number, which would make the number of connections to keep alive greater than the max_value for your connection speed, which would result in the error message you described. If your connection speed is MODEM, the number of connections will be set to 3 automatically in that case.