What happens if I share my iTunes ID and password with a friend who lives abroad? I would like to share my iTunes with my niece who lives outside the US. 

If I give her my iTunes ID and password, will she be able to listen to the music I have in my account? And more importantly, will she be able to access anything else other than my iTunes music?
This is a tricky question to answer as it depends on what you use that ID for. If it is just for iTunes Store purchases, then all she will be able to access is whatever you have purchased on the store. Of course, this isn't limited to Music, but also Movies, TV Shows, Books and Apps. She will also be able to authorise purchases using that ID and password and so could max out your credit card renting the Frozen movie countless times (I'm just assuming she's about 8 or so here ;)) or buying more hearts on Candy Crush.

If you also use it as your main Apple ID for iCloud and other Apple services, she will have access to those as well. Whether she uses it for those purposes is up to her; if she knows she is able to and is inquisitive, you might find her logging on to iCloud.com and nosing through your iCloud Mail or your Calendar.

The best option would be for her to have her own Apple ID and for you to add her to Family Sharing instead. That way, she has access to all of your past purchases, but will not be able to authorise any (you will be able to authorise on her behalf though). Additionally, she won't have access to your iCloud information.

If she already has an Apple ID, then great! If not, and she's under the age of 13, you'll need to create a managed one for her through iTunes. If she is over 13, you can simply create an Apple ID by going to the Apple ID management portal.

Have a look here for full information on creating an Apple ID for kids.