I am a White Sands addict, so I will do my best to answer your questions! I have stayed there at least once a year for the past 5 years.

The beach is quite large; not as wide as Coco (since the property is not as wide) but plenty deep. I have never had a problem finding space, shade or a lounge chair. The only time I would think it might be crowded would be during high season. That said, the properties next door are quiet, so I am sure that WS guests could use that area if necessary as overflow.

If you stayed at Coco, you might remember walking by the yellow balcony WS has in front of their bar.
Here are some views from the beach.
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If you are looking at staying in their standard rooms, I recommend the gardenside rooms rather than the beach rooms. As long as crossing the street does not bother you, the garden standard rooms are newer, larger and in my opinion have a better view.
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I have not used the wifi myself, but I know people use it regularly in their rooms, balconies, and at the bar/restaurant.

Hope this helps!