Hi, hard to say whats the realy reason.
The main request (index.php) takes a lot time and seems not be delivered step by step but only at once!
Did you install any plugin, that modifies the complete page content prior to delivery ?
This would keep the page as long unsend as the complete page code are build and at once parsed.
Also i found, that you work with session cookie. may be its used to track user and write back to database.
If there ist new code doing so, please be sure that writing to database will be done after all content been generated not in front of.
Mostly database need a lot of time for writing but are optimized for reading. So try to place monitoring at the end of footer, so the browser can start rendering content sent until here.
BTW: the calendar.css been reported by 404 Not found.
