How possible would it be for someone with some knowledge and experience of ASP, but 'expertise' in PHP, to finish coding my website in ASP? Are there any similarities?

Anything's possible, to put it simply.

There are people that know both, although I can't think of anyone off the top of my head (I'm not one of those people.)

I have only taken a glance at ASP code, and it looked as a simplified version of C++ code. Is it so flexible as PHP?

The major difference is as far as I know, that ASP is compiled code while PHP is interpreted code. That makes PHP more flexible at run time but not as flexible as JavaScript.

Compiled code is definitely faster.

ASP.NET code (in C#) is a version of C++. ASP is either VbScript or JScript (MS Server-Side javascript)

ASP.NET is compiled. ASP is interpreted

A PHP "expert" programmer would likely be slower at coding in an ASP language and vice versa.
I code in both but use ASP by choice and find I constantly have to look up PHP syntax which slows down the process considerably. Whereas with ASP, only functions I rarely use have to be looked up

Developers tend to sway to one language (for each area). You're best just looking for a ASP developer.