Custom php code in Word Press

I know it's possible to create a "custom template" in a Word Press environment. What I want to do is use the standard template of the Theme & then insert custom php code into the page.  I want to keep the normal header, menus, etc. of the Theme.

Does that work?

BTW, I want to use a custom form because I can't find a Word Press form plugin that will do what I want (without spending money, & even then I'm not sure)

Thanks