How to Prolong Lithium-based Batteries - Battery University
Some tips on extending your battery's life:
1) Don't drain the battery all the way down before you charge it. I charge when my phone's at 10% with the exception of #2
2) Drain the battery fully only once a month and charge.
3) Never charge the battery while the phone is on
4) Get an extra battery to enable the items above.
5) Get the official Samsung charger as it's optimized to charge the battery faster (about 2 hours from 0 to full charge).
For more details, go to the website Battery University
Good luck and have fun with your S4
To OP, read this yourself ^
I don't think discharging to 10% every time is healthy - it's almost a full discharge. Much better to charge far sooner, if possible.
No need to drain it full once a month...it really does not need to be calibrated that often. If you use the phone normally this will probably happen once in awhile naturally, though, so don't even worry about forcing it to be fully discharged.
You can charge the phone while it's on...just avoid doing it with the screen on for long periods of time as this will generate a lot of heat, which is the biggest enemy of battery life.
To answer your first question again: yes, it's absolutely ok! You actually WANT to charge it more often. Your battery will last much longer with a ton of partial discharges rather than full discharges. Charge your phone whenever possible, as long as you won't be using it actively for most of that time!
"Similar to a mechanical device that wears out faster with heavy use, so also does the depth of discharge (DoD) determine the cycle count. The shorter the discharge (low DoD), the longer the battery will last. If at all possible, avoid full discharges and charge the battery more often between uses. Partial discharge on Li-ion is fine; there is no memory and the battery does not need periodic full discharge cycles to prolong life, other than to calibrate the fuel gauge on a smart battery once in a while."
And to end...don't worry that much about your battery. A high quality replacement battery from a top-rated vendor like Anker will cost you only $12...so don't stress!