Do the propeller retention springs need to be replaced after a certain number of flight hours?

Should the propellers be removed if no further flights are planned for the day?

Is there an instrument for testing the propeller spring tension and what are the specifications for spring tension?

Where can replacement springs be purchased?

I've requested this data from DJI but haven't received it yet.

My thinking on this is that the props provide upward thrust, so after the copter takes off, the springs do very little. The upward thrust pulls the props tight against the motor clips and prevents the props from detaching from the motor clips...

Nope, but you need to check them before and after each flight!

You could easily check the length of each spring it it's relaxed position, i.e. no props fitted, or easier with a prop just sitting on a spring.  Maybe make a note and compare each week for your records.  If it ever started to lose tension by the spring getting shorter then that is the time to replace.
I have just measured mine from the top of the prop to the bottom of the strobe along the motor vertical axis.
Relaxed is              62,58
Locked                   59,88
Fully compressed 57,78
The springs are only being compressed by less than 5mm each time, so they will not be compressed beyond their yield point and enter plastic deformation.
And at one cycle per flight, if you remove the props each time you land, they will not fatigue in years or hundreds of years.  Think of a ballpoint pen retraction mechanism.