Laurie Ann,
As you have a car, the best idea would be to park for the day in Monterosso as there is parking available in both parts of the town. Don't forget to pack along an International Driver's Permit, which is used in conjunction with your home D.L. The carpark in the new town is probably the easiest. You may find this helpful - https://www.cinqueterre.eu.com/en/parking-cinque-terre . You won't be able to drive through the town though as it's a ZTL area. As I recall there are different roads to access the "new town" and "old town". You'll have to do a bit of research on that, or perhaps one of the other members of the forum can provide information on that.
After you've parked for the day, you can use the frequent local trains to visit the other towns. If the ferries are operating (weather permitting), you could also use that for a view of the towns from the water. Here's some further information - https://www.cinqueterre.eu.com/en/boat-excursions . The ferry dock is in the old town, just to the right on the other side of the tunnel. As I recall, there's a ticket booth right there and a WC next to the booth. The ferries stop in all the towns except Corniglia. Monterosso is relatively flat and it's not really a difficult walk between the two parts of town. Access to the old town is through an old tunnel.
There are good restaurants in both parts of town. One of the big favourites with many here is Cantina di Miky which is in the new town, close to the rail station. Don't confuse this with the restaurant Miky which is more of an upscale restaurant (owned by the same family).
Given your medical situation, hiking would not be a good idea. If starting in Monterosso, the Sentiero Azzuro trails have a steep climb at the beginning, and then a bit of a downhill slope leading into Vernazza. Only two of the segments are currently open, Monterosso - Vernazza and Vernazza - Corniglia. The Manarola - Riomaggiore trail would have been possible as it's mostly flat but that one has been closed since about September 2012 and won't re-open until about 2024 (that's the latest estimate but could change). And as you surmised, there are no WC's on the trails.