No, this phone does not "require" wifi access as it will provide its own internet access using Verizon's 3G network. It will be native coverage only which means no roaming ...service on Verizon-owned towers only. Verizon's native 3G network still has a very good coverage footprint, however.
So you have your choice of either using the internet access provided by the $45 Unlimited Plan OR you can also use wifi if in range of a suitable access point.
You can access the internet either way Sherry.
The Service Card provides for 2.5GB of data, plus unlimited calls, and texts for a 30 day period. After 2.5GB of data is used within 30 days, Straight Talk will "throttle" the speed until the end of the current 30 day cycle.
WiFi can be used at home, at hotspots, etc to help keep your data usage while on mobile(3G) down. A service card is not needed for WiFi to work.
No android phone requires WiFi and mobile data used simultaneously to get online using an android device.