jQuery supports IE 6 and later. However, if it's something a particular IE browser just cannot do, you may need to make your own routine for it for that browser to substitute another similar effect or make sure your code degrades gracefully in that browser. In some cases you must make sure you're working with valid HTML and/or have set any required prerequisite css on the element you're working on. Said css may not be required in newer more compliant browsers.
jQuery also supports all current versions of browsers, and most past ones that are still in use, even some that aren't.
jQuery is free for use by all under an MIT style license. Its .hide() and .show() functions are pretty straightforward. As long as they are used with the proper syntax, on valid markup, you should be fine.
There's extensive searchable online documentation:
And the code itself is hosted on Google's servers so you can use that. The latest version is generally:
If you put that in the head of your page before any code that uses jQuery you will have the latest version.
That's usually but not always the best version to use. Google hosts virtually all the versions, so you can specify a sub version or even a sub sub version: