MMS does not work over WiFi only. For many years, there was a workaround on Android that many OEMs (Motorola and LG, usually) took advantage of to be able to send MMS over a WiFI internet connection, and all other phones would just use an app like Textra.
Recently, Google enforced a new minimum API level on all Android apps in their store, meaning the trick Textra was using is now dead in all new versions. The only way to continue doing it is to have an old version of Android that did this natively, or to install an old version of Textra and never update.
Visual Voicemail is device-specific, and varies. If you let me know what device you're working with, I can offer a bit of troubleshooting.
We charge for voice minutes and SMS texts over WiFi specifically because our network partner charges us for those messages and minutes -- it's just that simple. Minutes used by Sprint customers do show up on their bill, but it's easier to say they're "not charged" for them, as Sprint offers "unlimited" minutes on their plans.
But no, the point of WiFi calling is not to avoid these charges. Our former VP of Product explains it a bit here:
Sure, you're not touching a cell tower if it's a Wi-Fi Calling minute or text. But your call or message is still traveling through T-Mo or Sprint's infrastructure — which do have real costs (in the realm of hundreds of millions of dollars per year for each of them, if not more). They do have to pay for the termination of those minutes and messages, and they also have origination costs, regardless.
If your internet connection was connected directly to the tower, it would be a safe bet to argue that those connections should be free, but your WiFi router only replaces the very first step in a LONG line of steps your phone call or text message goes through to be connected to the other party.
That's why we're big proponents of services that we do not bill you for. For example, iMessage and FaceTime (both iPhone-exclusive) do not touch the cell network on your end if you're using WiFi, so those are effectively free. This reduces the number of messages charged by Ting to iPhone-to-iPhone customers by a HUGE margin.
Facebook Messenger and Hangouts are two others (both cross-platform) that allow voice calls and messaging without incurring cost. There are hundreds of these kinds of messaging apps out there that we don't bill for (aside from data if used on-network instead of WiFi), and we even blog regularly about ways to hack the system a bit to not pay us for things like phone calls.