You have three questions here:
q: SendKeys is not working.
a: You need to check your gekodriver. Make sure its updated to have sendKeys work fine.
q: Key F11 is not working
a: Selenium is built using JavaScript as its core. When you press key F11, its not executed by JavaScript. Its executed by the browser. So, selenium may not support use of F11 and F5 keys.
q: F5 Key is not working
a: Instead of F5 I would recommand you to use refresh()
If you are ought to use F11 and F5 keys, I would suggest you to use thrid party tools like AutoIT.