Front end question

The best way is to use CSS preprocessors like Stylus or Sass and for the JavaScript par use compilers like Babel. With these tools, you'll get 99% coverage on the most used browsers.

Don't try to do it yourself, it'll be a waste of time.

Instead of saying "99% of users" I would say I want to support the last X versions of these browsers. You can see browser stats here - https://www.w3counter.com/globalstats.php. The question you have to ask is what are the browsers you want to support. As has been said you can either A) check out caniuse and roll/test the features yourself or B) use a compiler like babel and use babel-env to determine browser support, add required polyfills for JS, and use a css preprocessor to take care of styles, OR use a CSS in JS library like emotion

1. You can check your features against https://caniuse.com/
2. You can assemble volunteers to look at your site/app with their myriad devices and pay them with beer/cupcakes for screenshots of weird stuff. This paid off for me a lot in the past
3. Save your old phones/tablets. Curse when one of them shows you a surprise
4. Give up on some of the outlier browsers

That's quite a hard target to hit. Good start is to find out what device/browser combo are 99% of your users using. Then find out what fallbacks and polyfills you need to use and do a lot of testing. Preferably on real devices and seek opportunities to automate.

Probably nothing to be honest, because there are so many browsers, mobile devices, computer screens out there which covering 99% would eat up too many resources.
There are some saas tools out there for "cross-browser compatibility" testing, it if you don't want to do it manually.