How much LED for my 4x4?

It will be OK, but I prefer a bit more horsepower. I think 300 watts is good for a 3x3 but a bit lite for a 4x4. I want the capability to do at least 35 watts per foot and am typically about 30-35 watts per foot during flower. For a 4x4 tent I'd want the capability of going up to 500-600 watts. That doesn't mean your going to use all that power. I just like to have a bit in reserve so my new light isn't maxed out right from the beginning. With one light of any size in a tent that large you will have a noticeable hot spot in the center with drop off as you approach the corners. Instead I run two lights at reduced power. I provide the same wattage I would with one light but two lights spreads the light more evenly within the tent so there is less shadowing and the plants in the corners still get good light. And, if one light dies you haven't lost everything. You can crank up the power on one and get by until you get the other light fixed.

Yes! I have the tsw2000 and my first grow went wonderfully with just that light. I hot about 20oz in my 4x4 tent! For my second grow, I added an extra tsw2000 which gave me 50k-60k lux across the entire canopy (using the LUX app on my new galaxy phone). The buds were also MUCH better on my second grow. I think a lot of this was because I made n00b mistakes on my first grow, but I credit the second light a bit too. Little warning: adding the second light greatly increased the heat in my tent, so ventilation became key. Moving forward, I will use the single tsw2000 for veg and add the second in for flower. That all said, a single tsw2000 will work without issue in a 4x4 tent!

It will be more than sufficient and you will get more than with HPS. The TSW is older tech though, choose a QB with at least the LM301b chips. If you do get the TSW, dont put it too close, specially during veg, hotter lamp. So at least 50 to 60 cm away and on max 33 percent. Then on full for flowering and your get great results.

It should be OK. I use the ts1000 in a 2*2 and have to turn the power down a bit as it's a bit to strong for my tent.