Theme Customize not available

Hi WordPress community,

I have issues with this site
h t t p : / / f h i n c . c a / (without the spaces)

Some files in the FTP were accidentally deleted…making the site crash.
We contacted the host and he restored an older version but it is quite buggy.

I tried to fix it by accessing the dashboard and “customize”
but nothing loads. I thought of using CSS to re-arrange it but I am not sure if it efficient.

What would make the customize not accessible?
Is there a way to restore it?
The reason I am asking this is because I want to fix the logo, header and footer, among other things.

I didn’t create the site but the theme used is apparently
a “custom” (not sure what the owner meant) and outdated Twenty Ten.
If I update it, would i lose the custom setting?

Also, there are 2-3 different slider plug in, I tested 1 at the time, but none works (as you can see on the main page).

Again what would be the possible reasons for it to not work?

I know some HTML CSS
but not too much of PHP and MySQL

I hope it is enough information to troubleshoot this.
Looking forward to see what are the options.

Cheers!