Aaah, ok. Good question, and not an easy one to answer. You could try installing munin as it should show any memory spikes, etc. Simply accessing an image on the server should just give a not-found error, not a crash. It's possible that the invalid characters are causing apache to fall over, can you see the GET from the access log using timestamps to match it over to the restart? If so you could try telnet'ing to port 80 and doing a manual GET to see if that causes it to fall over. At least that would start to narrow it down.
You might also want to install mod_security or some other forward facing proxy to capture requests that are coming in, this might help you in figuring out what kind of request is causing Apache to crash.
As for your other question on telnetting commands:
mini-me:~$ telnet google.com 80
Connected to google.com.
Escape character is '^]'.
GET / HTTP/1.1 <-- what you type in, followed by a blank line
HTTP/1.1 200 OK
Date: Sat, 18 Nov 2006 10:45:46 GMT
Set-Cookie: PREF=ID=c1262de97f1dd9b8:TM=1163846746:LM=1163846746:S=RtatJurljEDXCisc; expires=Sun, 17-Jan-2038 19:14:07 GMT; path=/; domain=.google.com
[ .. snipped the rest .. ]
In this example the request is for / (the index file). General format is:
Before your post I checked some php related files that had blank space I removed it and have not had a restart since! I am monitoring it and will definitely implement the test should it arise again. Thanks.