Is it possible to search mail for strings? Is it possible to perform advanced searching on the native iPhone Gmail client? Search for mail containing "some string" or mail sent by, from?
Yes, yes it can.

You can do any search that gmail supports:

from:myemail@mydomain.com "searchtime" produced the following search results (which are correct):



Examples of what you can do:

subject:(Search Term)

To exclude a term you can do:

-Windows

And pretty much anything normal Gmail supports.