Hi there!
Thanks for joining Guitar Tricks!
The best way to improve rhythm is to use a metronome, and practice playing an actual song. You can always practice with our web metronome right here: https://www.guitartricks.com/toolbox.php
You can also check out this lesson on rhythm right here with Anders: https://www.guitartricks.com/lesson.php?input=19989&s_id=1568
Rhythm is all about feel, and if you're new, you have to get used to not playing too fast or slow. It takes time! (no pun intended)
Fingerpicking does not require finger nails, a lot of people simply use their finger tips, but if you got strong, long nails, it may help a little bit. This is a great lesson on Travis picking, one of the most popular styles of finger picking. Check it out here: https://www.guitartricks.com/tutorial.php?input=1774
I hope that helps!