'Nother newbie MOSFET Query

First a brief but profoundly sincere "Thank You!" to all the individuals here who selflessly and generously and PATIENTLY share their knowledge and expertise with the rest of us.
Now then,
I managed to get my IRF7413 8 pin SOIC package soldered to a little board and PWMing some LEDs, but I needed to know more so I read through as many of the MOSFET threads and as I could, (would "MF'ers" be an acceptable abbreviation?) and now have a much deeper (but very incomplete) understanding of their differences and characteristics. One important item I learned was the need for the series resistor on the gate to handle the on/off capacitance thing, although my circuit without one ran for hours and hours. What I didn't find understanding for is this:
As long as I run the same number of LEDs per drain, I can run up to 6 per, total 24. If I try 3 on one and 4 on the others only the three will light. I think it's because the 3 LEDs are 'clamping' (not sure that's the proper usage) the voltage to low to light the others? Can this be overcome and how would this apply to driving multiple motors, I'm guessing they need to having matching specs and will run somewhat synchronized ? What other ways can the 4 drain pins and 3 source pins be manipulated?

The need for a resistor on the gate is to protect the Arduino pin from over current during the switching transients. I MOSFET gate is a capacitance and thus presents a very low impedance load (an ohm or less) to whatever is driving it (until the capacitor has charged up).

This means the Arduino pin will be beyond its maximum ratings for a short time (a few us at most). In general you get away with this because most of the time there is no current flowing and the output transistor gets to dissipate the heat from each pulse.

However you are taking it outside the specs which is not the route to a long and reliable circuit life. A 150ohm resistor will fix this.

If you want to switch at a really high frequency you need to keep switching times short to avoid switching losses in the MOSFET, so you need to use a MOSFET gate driving circuit that can supply more than 30mA (anything up several amps for big MOSFETs with big loads).

As for the LED behaviour you describe I can't figure out what your circuit is. In general if you place LEDs in parallel they won't get the same current, and if they are different (colour, brand, model or even batch) then this difference can be orders of magnitude. The way to get the same brightness is to drive them individually, or in series, setting the current they receive (rather than the voltage). The easiest way to do this is to run from a higher voltage than they need and use a current-limiting resistor to approximately stabilise the current. The more sophisticated way is with a constant-current driver chip.

Sigh, just spent 20 minutes on a detailed reply/description of circuit, then hit something wrong and lost it. No time to rewrite the whole thing now, but yes my LEDs are in series with a 270 ohm R. So the drain/source current is proportional to the gate voltage? Did I say that right? That's how I see it now. More later. Thanks again.

...but yes my LEDs are in series with a 270 ohm R.

In series, the voltage gets divided across all of the series components. LEDs basically "turn on" at about 2V (depending on the LED). And, the voltage holds at about the same value when you increase current. Essentially, the resistance drops as you increase current.

If you put 3 LEDs in series, it's going to take about 6V to turn them all on, plus you get a voltage drop across the resistor. This is OK as long as you have enough voltage to "spread around", and as long as you calculate/measure the voltage drop across the resistor to determine the resistor value (using Ohm's Law). With more voltage dropped across the series LEDs, there is less voltage remaining for the resistor. This means you need a lower resistor value with more LEDs.

If you put 3 LEDs in parallel with the same current-limiting resistor, they might not all glow at the same brightness, because although they all have the same voltage across them, but they may have slightly different resistance characteristics and therefore may have different currents flowing through each.

So the drain/source current is proportional to the gate voltage?

I think so. (It's been awhile since I studied MOSFETs.) But, we are often operating the MOSFET in "saturation", where the current is limited by a resistor. We are using it as a switch, where it's either full-on or full-off. When it's full-on, the current might "calculate" as 10 Amps, but your resistor (or other circuitry) might limit the actual current to 1A or so...