If the phone supports GPRS it doesn't mean that phone would support WAP Push. So the phone has to be WAP 1.2.1 compliant to support WAP Push. Only exceptions to this rule are Nokia 3315, 3350, 3395, and 3410, which are WAP 1.1 compliant but also support WAP Push.
Answers to your second question is no. For example Nokia 3650 is WAP 1.2.1 compliant phone but it also has XHTML browser.