You will unless they are closely related enough to give you citizenship rights. Nationality law is completely different from country to country within Europe, though.
Depends how she got citizenship. If she got it through bloodline, maybe you're eligible too. If not, you can come as a tourist. Probably 3-6 months, depending on country. May be eligible for cheaper visa if you'd supply an invite from her.
Keep in mind that major non-EU countries (US/CA/AU/etc) don't need visa for tourist stuff. You'd get a stamp at airport for x months and that's it.