I was requested to send login details and after that I'm not sure what the author actually but yes he may have applied some fixes. All I know is the theme was updated. So I would suggest others facing similar problems to please update the WP core and also the theme to updated versions. Thanks.

This was a theme error actually. After failing all tests I asked the theme creator to inspect and he fixed it and acknowledged the error. Thank you.

@kaiser Tried debug bar. But didn't come to any help since the problem is when the site is not connecting. And I have also figured out thats a theme issue. When I'm changing the theme to Twenty Fifteen everything works smoothly! Question is how can I investigate & apply appropriate fixes? Thanks.

@kaiser Strangely the problem sometimes completely disappears. Can you tell me how do I troubleshoot without messing around? I've wasted a lot of time. Thanks!

But I merely updated my WP to 4.5 recently. What do I do now?

But then host says it is a WP error. I have included their response in my answer above. Please check.

Yes. But my admin panel is working great. Please check response from host above.

Yes my question differs. That is the present structure of my 'quotes' multi site where 'authors' is the tag base, and categories like 'Startup quotes' are simple categories. The current urls has got thousands of fb shares, good rankings. I am migrating to a new conventional wp setup (not a multi site). Question is will it be at all feasible to duplicate the multi site setup in a single wp installation ? (The scope of question changes to some extent) Or should I post a fresh question not limited to custom taxonomy archive? Apologies for the confusion.

No success. What I really need is, /quotes/this-is-a-quote.html + /quotes/authors/some-author/ + /quotes/startup-quotes/ What are the other possible solutions to implement this? Pls suggest.

Gimme sometime to try this out and get back to you!