Controlling 1000W LED strips with Arduino using PWM and MOSFETs
I see no reason this wouldn't work.  If you're concerned about the effects of a PWM load on your power supply, I'd suggest adding some extra capacitors on its output (I don't know how well the output is filtered already, but more capacitance never hurts in a power supply).  Your MOSFETs seem appropriate for the job; the HA210N06 on that board is a new one to me, but this datasheet  suggests that they will be fine.   However thermal dissipation could be an issue: at 5V gate voltage, the channel resistance will be about 6mOhm, so power dissipation for 15A will be about 1.5W.  Even at 20% duty cycle, that small heatsink will struggle to dissipate an average of 300mW. I'd suggest fitting a larger heatsink or a small fan.  And if you can use a smaller MOSFET to boost the gate voltage up to 10V the channel resistance will halve, which will help a lot.  I certainly wouldn't trust the ebay vendor's description that the board is stable up to 25A: there's just no way that tiny heatsink can handle close to 2W.

The Arduino Uno board has 6 PWM outputs, which can be set to run on different duty cycles, phases, and IIRC and up to 3 different frequencies, so arranging for appropriate power sharing between your circuits should be possible.

Multiple MOSFETs in parallel (not series) works in theory, but in practice variations in manufacturing etc will likely cause one of them to take a lot more of the load than the other, so one will get hotter than the other.  If you can arrange to split your load into two separate 15A channels, that would be much more reliable.