Running 2 strips from 1 board and basic understanding questions

I am following this tutorial: https://learn.adafruit.com/rgb-led-strips/current-draw

I have strips with 30 led/m, stp16nf06l Mosfets, a 600mA power supply (which I will upgrade later on, this setup is just for testing purposes) an Uno and a few 1k resistors(I only have those left). My question being: When and why do I need the resistors inbetween the pwm pins and the mosfet? And will 1k resistors work aswell? (I saw another tutorial which was pretty similar to adafruits, but they were using 1k resistors.)

2) Can i control multiple strips from an uno? It certainly has enough pwm pins. Should I just buy everything again and make the same setup or can i use the mosfets i have right now for 2 strips somehow? Also: Does it make a big difference if I power the second strip through 2-3m long cables? What do i need to pay attention to? How thick do the cables need to be to be able to handle a 10meter strip (~6A). Thanks in advance.

With MOSFETs, it's not critical to use gate resistors. The current required depends on the pwm frequency, not the current drawn by the strip, as it would do with bjt transistors. Some MOSFET drivers use pwm frequencies of several tens of kilohertz, which means driving the MOSFETs can require quite high current. But arduino pwm is is less than 1KHz, so not much current is needed. But using resistors will probably help give the Arduino and the MOSFETs a long life, so why not?

The value of the gate resistors is not critical. Anything from around 220R to 1K is fine.

Yes, you can connect several strips to the same MOSFETs in parallel, as long as you don't exceed the total current rating of the MOSFETs. If they get too hot to touch with your fingers, attach some heatsinks to them. If they still get too hot, attach a bigger heatsink.