Yes, eero should work fine with the T-Mobile internet as long as they provide internet access via ethernet port for the head/gateway eero to hardwire into.
You can also use it for the Internet Backup feature we now have: https://support.eero.com/hc/en-us/articles/8947860842523-What-is-eero-Internet-Backup-
No... Unless using Access Point mode and even then, Eero still has issues with T-Mobile Home Internet. TMHI is a ipv6 only service and does not passthrough the ipv6 normally to a router. It uses CGNAT to create virtual ipv4 addresses. Because of this a router needs to have ipv6 passthrough or bridge mode (called different depending on brand). Eero & Google Nest do not offer this feature. Therefore you would be forced to use in Access Point mode to get full features of ipv6.
And I would know, because I had Eero but switched to TMHI and Eero was awful because of the lack of this feature. I ended up having to go get TP-LinK Deco's which if you read on reddit is the routers with the least issues on TMHI. But again, it's recommended to use in access Point mode for the least issues. TMHI works great and is fast but the way it was built, makes things very breakable on routers. I see speeds between 250-700mbps download where I live with TMHI depending on the time of day, etc... But it works for me.
I was very sad Eero has not commented on bringing ipv6 passthrough/bridge mode to their routers, months after is was requested. Not even a update or comment if it can be added.