Ad1. Just after make minification, do some tests with development tools (F12 in FF) There is a console where you will see all errors, warning etc. If something went wrong, you’ll see it
https://developer.mozilla.org/en-US/docs/Tools/Web_Console/Opening_the_Web_Console
Ad2. Hard to say because every case is different but sometimes it’s matter.
Which plugin do you use for that? For example in W3 Total Cache you have an option which let you make order of your scripts for minification