Sentence Meaning – How Different Are They? Vs. How Are They Different?

Both are correct, but the meaning is quite different.

How would I know her age without asking?

which is saying you can't determine (in your mind) her age; to know you would have to ask her. It regards an intuitive ability.

How can I know her age without asking?

which is like saying "How can I (find out) know her age without asking? This is more of a technical question; what process can I follow. It is a how-to question.

Interesting question.

Rhythm can refer to the stopping and starting or speeding up and slowing down or
ebb and flow of something.

For example, if you are awake during the day (which is usual) and your friend is awake during the night (sometimes referred to as "being a night owl") you both have different personal rhythms (not to be confused with circadian rhythm.

Pace is usually used to describe constant speed while travelling, either literally or metaphorically

The runners ran at a 4-minute-mile pace
The pace of life inside big cities is hectic

You two may be missing each other because

your rhythm is not at the same pace as your friend, or
your friend's pace does not have the same rhythm as yours

Obviously, pace and rhythm wouldn't match since they mean different things, but by using them you both may be suggesting that you view your daily lives in different ways.