Hi Bernoull!!
What's your definition of flying alone? No instructors or no passengers?.
Either way, there are two ways in which you can obtain a private pilot license. Under the Federal Aviation rules part 141 and part 61. For part 141 you need less hours, but I did it part 61. For part 61 you need at least 30 hours of instructon and have to fly for at least 10 hours completely alone (no passengers allowed) before being able to obtain your private pilot license .
For me, flying alone was CRAZY scary the first couple of times, specially on your first solo flight (gotta do 3 take offs and landings). I cried before going cuz I was too scared hahah. However, I would say my first solo was one of the most happiest moments in my life.
When you need to do your first solo cross-country (a flight for about an hour an a half, depending on the distance) it's pretty scary as well. I started to hear new weird sounds on the airplane haha.. but eventually you gain confidence and get to know the airplane and yourself very well.
Also, my dad is a pilot and when we were little we had an accident while landing and I was TERRIFIED of landings since then. But I still remembered the joy of flying and traveling and eventually forgot about that and now landings are my favorite part. Oh and I'm also afraid of heights, and you'd be surprised but most pilots I know are afraid of heights as well haha which I find funny. So if your fear of heights is what's holding you back, don't even think about it and give it a try.
About the safety of the airplanes. It's relative. Bigger airplanes are considered safer because they have more backup systems, and airplanes with more than one engine are considered safer because if one fails you have the other one. But this doesn't mean that small/propeller/single engine airplanes are not safe. Think about it, a Cessna-172, is the most common airplane used for training pilots. Think about all the students who are learning to land for example, all the mistakes they make and at the begining their landings are generally HORRIBLE and still Cessnas-172 from the 70's are being used and overcome all of the pain the students have them go thru haha. That tells me those little airplanes are amazing...
Plus..if you are flying around and your engine stops, it's not like the single engine airplane is going to go down inmediately, the airplane glides and there are procedures that you are taught to take advantage of that and be able to save your life.
So..if you are thinking about learning how to fly... don't even think about it for a minute!! and do it as soon as you can, you'll love it!!..If you have any more questions you can always PM me I'll be happy to answer them... 🙂
PS: sorry about any grammar errors or anything..3 am and very sleepy lol 🙂
