There aren't really any differences between Scrum and other approaches, for this.
Is the team running at maximum efficiency?
There's no real way to tell if they're at their 'maximum' (and what does that even mean? If a Team goes insanely overworked for a week and gets lots of work done, and then all die from stress-induced issues, is that 'maximum efficiency'?), however you can gauge efficiency by just measuring their output and comparing it to some standard (previous efficiency, other Teams', etc.)
Is the team improving over the time?
Very straightforward... just measure output over time.
Is the team motivated enough?
Highly dependent on your role in relation to the Team. If you're their manager, I'd suggest regular 1-1s where you encourage them to bring up any issues. Attending Retrospectives can also be invaluable, especially if 1-1s are infeasible. Just make sure you're only attending, not participating. You're not part of the Team, so don't take over their Retrospective.
Is the team meeting their commitments?
Again, straightforward... The Team makes a commitment every Sprint. Do they meet it?
Is the team meeting coding standards?
Again, straightforward. Look at their code. Does it meet the company's standards?