Tim for your page to be faster you may decrease the number of items in blocks like latest videos etc. in the Latest Videos block there are 28 videos if I didnt count wrong.
For every block try decreasing them reasonably.
the rewrite error is not an error, I have the same in my studio, I use nginx and it says rewrite is not enabled.
another way to speedup your homepage for the visitors could be creating another home page for the visitors only and enabling page cache from studio.
(with page cache enabled some css like page layout or some javascript may not work properly, to be sure you may just try/see).

by the way your home page seems quite fast :)