Is it normal to be scared of space?

This may be part of your insecurities in relation to being able to control and/or understand things. Since the cosmos is so vast and huge, you fear it because you have a hard time controlling it or understanding it. Am I right or wrong?

"The fact that space is so big..."
Is incorrect.
'Big' and 'small' are relative sizes, that are not used in physics.
Space is infinite, and infinitesimal. Space, however, does have a finite quality, due to the existence of proto-quarks, quarks, quarkenergy, massenergy, and the preceding latter three corresponding antiparticles thereof, in space.

"I get scared thinking that after we die we are basically immortal so again the fact that there is no end to time,..."
Is also incorrect, on two fronts.
So-called 'immortality' is a fallacy. Every life form in the Universe, no matter how resilient, does, in fact, have a life span. The only hope for long-term survival, is to keep moving, and to continue reproducing.
'Time' is an abstract concept that does not exist, in reality. There really is no beginning, nor no end, to time. It could also be said that 'time' is always beginning and always ending, because 'time' is a relative 'property' of massenergy, and massenergy particles frequently form, annihilate, or are absorbed into other massenergy particles.

Now do you feel better?

*Please note: Proto-quarks, quarks, quarkenergy, and the latter two corresponding antiparticles thereof, also have an abstract 'time' property, but this is meaningless to ordinary life-forms in the natural Universe.

You are someone who runs off being in control of her situation. The thought of loss of control clogs up stability. I get this way when I think of roller coasters. Just beware of people who feed off convincing you to lose control and keep things consistent. Get a hobby like maybe find a book you can get caught up in.

Well, i try to make the best of my limited existence as a human being on this planet we call earth and hope to contribute in some philanthropic way, developing a social conscience in the way to improve myself and help others in the same way.

To address your specific concern about the threats of space, of course its haunting, you'd froze or burn to death and would die from oxygen depletion, but space aventure into the unknown its something mankind has got to look forward to in the future. There are many wonders and perils outside of our home sweet home.

I'm an atheist and a man of science, so i don't believe in the afterlife, we are living conscious multi celular organisms, when we die that's it, its like you had never existed in the first place, all that's left behind is your legacy, so stop worrying about the long term future and strive for a better present, preserving this earth for the future generations to come.

Don't think so much

Watch Doctor Who. It will make you feel a lot better about space and time.

I don't know if it's "normal," but space scares the crap out of me, too. As does the ocean. Just the idea of a vast space out there so much larger than anything I can even imagine, and with so much unknown. Perhaps "scare" isn't the right word, since I'm not really afraid. It's more of a creepy feeling. It creeps me out.

Whatever space is, whatever afterlife is, they exist whether you get anxious or not.

There are billions of people, some worry about this, most don't.

But a person's thoughts have never changed these things.

If you want to think use it for something you can effect.

I don't believe in space.

Both of these are the great unknown, space and death.

We know (comparatively) so little about the universe still. We have some amazing scientists who have made discoveries about it and are speculating on what's further out there, but might never understand it fully. I used to get these feelings when I was a child, that space scared me, but the more I've read and heard the more it actually excites me, the possibilities of it, what life might be out there.

Death is so final, on the other hand. There might be an afterlife, don't know, will find out when it happens. Worst case scenario you just end up going back to the same state of non-existence you were in before you were born.

yes!! me too! and death like where the fuck do we go or are we just dead and our entire soul and life is gone?? weird. freaks me the fuck out

Well, it is "... the final frontier".

It's fun to think about what kinds of life/entities live out there.

And will they make contact with us, or smash us to pieces, maybe keep us alive forever in horrible experiments of torment?