- Is threading the appropriate tool to use or should I use fork instead?

I tend to prefer fork, but threads might be ok

if the server's maximum number of simultaneous requests is set to 10, If the script is not interrupted I should not be able to access the server using my browser right?

No. The server will serve up to ten requests at any time. But it won't take long to serve login.php, and once it's done with that, a slot is freed, for the next request to come in. You with a browser, or your 10-thread script might be the next to be served.

- Memory wise, is there any way I can alleviate the memory usage?

If you think your threaded script use much memory, try with forking. I think that forking usually consumes less memory, but I don't know if that is universally true, or if it's improved in 5.10