Q1, Best thing to do is search and read reviews. (Some are better than others yes.)

Q2, As I recall they do state compatibility with mesh systems. (Some maybe better than others.) On the community page at the top is a search box. Us that to look for references to the names of different mesh routers and see what hits you get and digest the information. Another source of information is the Reddit forums as lots of people have opinions and post out there too.

Q3, Now that is a loaded question. Maybe and maybe not. I only say this as it depends upon your proximity to a T-Mobile cellular tower and the available cellular signals plus a few other variables. If you are in a location where there is a clear, strong, clean signal from an n41 signal source you can get some pretty impressive speeds as long as the cell does not have too much load. It really depends on multiple factors so I will not say, sure you bet ya. The truth is every location is unique and you will only know what is possible by testing and confirming what you can. 

One thing to keep in mind is that the T-Mobile gateway is a wireless router in effect. It is very limited as far as configuration options so a mesh system or router for other personal needs may be necessary to meet what you want. If your needs are not that demanding the gateway might be enough. I run the original 5G Nokia gateway and well it meets our needs. It may not meet all my wants but it does what I really need. It is a place to start. If you make a test run with the gateway for the trial period and like what you see then consider what else you might want to spend on. Just my take. If you need remote access from the outside in and need port forwarding and have exotic gaming needs well do your homework as port forwarding is not going to be working for you more than likely. Some services work quite well but some others just cannot work. Some people have success with some services using a VPN but that is yet another cost factor to consider. 

Speeds can be pretty impressive. I can get 200-300 MBs down and meh… 25-35 MBs upload speeds or more at times. It is plenty for streaming videos and we can exercise multiple streams at the same time and my son games on his computer. So, it really depends upon location, the cellular source, traffic volume, and other variables. Just like any other cellular vendor the external factors do impact service delivery so nothing is perfect all the time.