They are actually owned by Deutsche Telekom and Vodafone has no part of it. There were some internal problems for a while with T-Mobile US a few years back as far as the 3G expansion and it's profitability. The HSPA + Rollout is great but T-Mobile needs to do something to get a higher ARPU per Sub.
If they merged with sprint they could become a powerhouse and it could boost their earnings. And pretty much Sprint is the only company they could merge with because a merger between AT&T would not be approved because it would be too big.
You are right Deutsche TeleKom is the new name for what was the Deutsche Bundesposte. ie the main German carrier. I have been around too long.