Put a lot of plants in, good lighting and relatively low fishload and there isn't a huge amount of maintenance needed beyond feeding.
Looks like it could use some pruning though...
How far are you planning on moving them and how thick of substrate? It will certainly add a lot of extra weight. To another room you might be able to get away with moving the whole stand together if you've got 4 people. To another house...Just completely tear it down.
Bigger motor=more flow. More flow=more crap caught in the filter wool. More crap=clogs faster. Clogs faster=loses flow faster.
Have you tried removing the filter wool? It's not a necessity. And it could be that the eheim filter or the difference in how you've put it in also means that the water in the eheim just bypassed the clogged up filter wool while the fluval still has to push through it.
Look at the flow chart. 2 feet of head is roughly 1 PSI.
I'm assuming that means that it won't open with less than .5psi? So as long as your pump has a maximum head of 1 foot it should provide enough pressure to open the valve. Which...6000LPH I'd imagine it has far more than that.
Yup, sounds like wireless issue, not the internet connection. Try running a speed test in your lounge and another with your laptop sitting next to the router and post the results. I'm actually curious about the results.