Well, you don't tell the hostess what to do regardless. She can make her own choices as to if she needs firm RSVPs or not. You also do not have any involvement in the planning of your own shower or the tracking down of guests.
Personally, only about 50% of the showers I've attended even requested an RSVP, anyways. So if your hostess needs them, she can ask.
What about RSVPing to the wedding? Should I email or call people?
Wait about a week after the RSVP deadline. You call or email your side and FI calls or emails his side. Use your best judgement as to how you normally communicate with those friends/family. Some people are much more quick to answer an email than a phone call and vice versa.
If your parent(s) are the hosts of your wedding, you should ask them first if they'd like you to assist in the RSVP follow-up calls.