Let’s say I just finished (it never is, right?) writing a web application. I did my best applying what I know to prevent any security issues.
But how do I find out if what I wrote ís actually secure?
Are there any (free?) tools available?
Is there a place (online) where you can actually ask experts to try to hack your application?
Your question suits better at security.stackexchange.com
There is one already answered by many:
https://security.stackexchange.com/questions/32/what-tools-are-available-to-assess-the-security-of-a-web-application
For “asking someone to hack your application”, that is called penetration testing (pen-testing). I doubt if there’s any free service around. Just Google and pick your service provider.