Will using my own router resolve some issues with the T-mobile router?

Personally, I think using your own router will resolve issues. I simply plugged my eero 6+ into an ethernet port in back of the T-mobile gateway and it worked.  I only had to sign in my network password with various devices, even though it was the same eero password as before.  Try your router and see if it helps. If not, go back to using the gateway as a router. 

I am fed up with T-Mobile home 5g internet..2 different gateways the round grey one saying connected with no internet...now I have the square black one saying connected unable to provide internet.....I spent all weekend on the phone in the store back on phone for hour or so doing every test they could think of no answers..not it's going to the engineer's....one last chance and I'm finding someone else 

As a new T-Mobile Home Internet customer, I too have encountered some problems. The issues stem mostly from a customer’s inability to access any meaningful settings on the gateway. I have an Arcadyan KVD21 5G Gateway that T-Mobile provided (the square gateway, not the cylinder). One issue right off the bat is DHCP. If you have an existing router hooked into your cable modem, or an all-in-one unit from, say, Xfinity, you can configure DHCP. It's the same with the Verizon and AT&T gateways.

Not so on the Arcadyan KVD21 5G Gateway. As I'm sure you know, you can only have one DHCP server on a network or you will have problems. Therefore, the only way to add a router to the gateway is to use the router as an access point only.

This lack of transparency into the Arcadyan KVD21 5G Gateway (and others) was to make the connection to the T-Mobile network as painless as possible for the average user. Unfortunately, that results in some problems to users who want to customize their installations. As an example, there is no Network Address Translation (NAT).

I can't speak to why a VOIP solution like Magic Jack wouldn't work, but it might have something to do with the access to the Internet that T-Mobile is providing. Unlike a cable modem or DSL, which connects the customer directly to the Internet, T-Mobile connects via a cell tower that also uses voice and data transmissions for it's customers. My guess is that the protocol(s) that Magic Jack uses are incompatible with the cell tower you're connecting to.

As for not connecting to the T-Mobile network (no Internet), can the T-M store connect when you bring the gateway into them? If so, then the problem isn't with the gateway, it's with your geographic location and/or placement in your home/office.

My TMHI is working very well for me in S. Florida, although I was hoping for more speed. For now, I'm connected over 4G LTE, not 5G, but I think over time that T-Mobile will continue to expand their network and enhance their services. I believe this because they are in competition with Verizon, Xfinity, AT&T, Hotwire, et al, and they need to provide services that will drive potential customers to use their service. Hopefully some of the issues you're experiencing will be resolved in the near future.