Yes. Yes, there can be residual dysplasia, it is important to follow up closely with your physician.
Yes. That's the main reason we repeat pap smears 3 months after treatment, looking for residual or recurrent disease. Low-grade disease can be followed since half can remain, 1/4 will regress, & 1/4 may worsen. Follow your doc's recommendations if you have persistent disease. Good luck.
Yes. But 3 months may be a little early to expect things to completely clear. A lot depends on how abnormal the pap is and what the hpv status is.