it's another one of these tense things, but the nose remains towards the mat so the back isn't arched, and you have to lift your arms up from the mat and move those.

But your head and your shoulders/arms are off the mat, at least?

Probably to measure progress with that one you'd have to time how long you can keep up this kind of arm position.

Yup. With a bunch of exercises, you'd aim to do a static hold for a fixed amount of time (then rest for a bit, repeat, rest, repeat -- three sets is a good rule-of-thumb amount). As you get stronger, you increase the number of seconds you hold them for.

I have a cheap watch with a stopwatch, and plonk it on the floor somewhere where I can see it. Other people will set a timer that beeps when their time is up.