You may need to spend a little time learning how to read logs. Practice with logs from the site that is working as intended. You need to distinguish between
#1 intended errors:* anything intercepted by mod_security is a very evil robot trying something BAD. If mod_security is preventing your ordinary code from functioning, you need to either change a setting (not ideal) or fix the code so it will run without punching holes in your security. The same goes for anything that got a 403. If it was supposed to get the 403, everything is fine.
#2 unintended errors: "file does not exist" (404/410 message) may be just that, or it can mean that you made a mistake in a link somewhere.
In your case, all those timeouts from assorted IPs-- including three attempts from what looks like the bingbot-- are the root of the problem. Or rather, they point to where the root of the problem is. You need to find out why your script is timing out. Is your time limit simply too low or is there a problem with the script file?
* People who have their own servers may need to be reminded that error logs in shared hosting generally list all 403s and 404s. Log levels aren't set separately for each user so you have to compromise.