Overall, traveling in Europe is as safe as when you're living your day to day life back home. As long as you don't put yourself in stupid situations like walking down a dark alley late at night when you're drunk, you'll be fine.
Be aware of your surroundings and don't stand out
by flashing your valuables around.
1) Safe for women?
Absolutely! In fact, as you travel you'll come across many women who travel on their own and are having the time of their lives. Again, it's just like walking the streets back home except those streets may be cobblestone and the people walking on them are speaking a different language.
2) Solo Travel
It can be a bit daunting traveling solo for the first time. That is, up until you arrive at your first hostel. You'll quickly find out that you're never truly "solo" because you'll always find people to go on adventures with at your hostel.