Cache Weirdness and Site Speed

Hello SI Team

I could really do with some help here.
I have some weird cache issues.

eg here:

https://stackideas.com/forums/where-is-the-easy-blog-menu-coming-from-on-mobile-devices-only

Or for example over the weekend when I was testing on a mobile...

I kept getting this message:

"The most recent request was denied because it contained an invalid security token. Please refresh the page and try again."

Or if I go to my Vanilla Template and enable "Compress CSS" the formatting gets missed up.

Or if I go to my Vanilla Template and enable "Compress Javascripts" other stuff gets messed up eg:

The product description for Hika Shop Products eg:
https://www.finalbug.net/store/course/fcpx-media-foundations
Ditto the connection to FastSpring when you click "Finish" with "Compress Javascripts" on the Pop up Store does not pop up.
(I think the later must be the “FastSpring” Plugin that probably has some Java Scrip in there)
JA Promo Bar (Count down gets messed up/guess this is Java Script again)

Probably more things?

I know that this is all a little vague but could some one at your end look at this for me.

I also have JCH installed but it just seems to make things worse so I have disabled it.

Bottom line is I think some one from the Stackideas team might just be able to get to the bottom of this and maybe even help me:

Get my site working with less hiccups
And maybe, just maybe faster!?!
(And yes I am on a shared hosting environment until I can afford the dedicated way)

any insights gratefully appreciated

Paul

ps please note FTP details are up to date :-)