How to implement cross-browser compatibility?

Question

Cross browser

Hello!
Please help me fix various cross-browser issues.
Here is my work: son.topdetal.com.ua/mobi , works well in FF.
But the problems:
1. In chrome, opening pages with a script (hereinafter, the word page means what opens by clicking on menu items) works every other time, in safari the script does not work at all.
2. The "contact" button has erratic behavior on :hover.
3. after the page is closed, it, in the closed state, loses the display:none property; prntscr.com/9c7sqf and overlays other elements.
4. at a narrow resolution, when the content height is greater than the screen height, the page is stretched only to the screen height prntscr.com/9c7vrj.
5. problems in ie prntscr.com/9c7yzz
6. if you put 90 here properly, then after losing the :hover element disappears prntscr.com/9c82dn .
7. well, in safari it is generally not clear what is happening http://prntscr.com/9cpmth and JS does not work at all.
These are my problems. I would be very grateful if you could help me figure it out.