Is it normal that every time i close doors i feel something closing it for me?

Personally I do not believe in ghosts but my friend does and she says there are two possible explanations of this phenomenon that you mention:
1.Some ghosts are terribly shy and they need privacy, therefore they want to get the door closed as soon as possible.
2.Other ghosts might have had very bad experiences with burglars when they were alive and so they want to have the door closed for obvious reasons very quickly. In my country these ghosts are called "Bramo" and some esoteric groups here have even made up a spell for them "Bramo - zavírá samo" (translated as Bramo closes the door himself).
But as I say I am no authority on this as I do not believe in ghosts, bramos or others.

It is physics and some mind calibration issues.. ur mind thinks the door is too heavy and applies force more than required, and the feed back that you get is door being pushed with some other force or someone else, don't worry its you closing the door.
And one suggestion this scenario gives out hints of absent mindedness in a lil way, are you going through some kinda stress, if yes, do some stress release exercises...

Well that is too awesome I'm afraid

And I forgot to mention that sometimes the door handle even turns before I turn it! It happened again like 5 mins ago with my linen cupboard door...

Oh. I know that. I had that. And not only that.

When I was about 11 till I was about 19. I also had doors open for me before I managed to touch the handle, I had someone touching me on the shoulder or the back of my head, while being alone, I saw things in the mirrors, in dark corners and behind the windows, I heard whispers and shouts, and after a few years I even learned to feel someone's presence.

After I got tired of being tormented in this way, I started searching for answers. The church (Christian and catholic) was no help at all, the books on ghosts and demons were just rubbish, the internet was full of garbage information. But I did find copies of books on mysticism and spiritualism. Old but common books, like the "Key of Salomon" or the "Grand Grimoire". I approached them as philosophical works and learned to look at the reality in terms of "physical world" and "spiritual world". The lectures convinced me that whatever I might have been experiencing could either be demons or ghosts or even schizophrenia. I scratched that last one out, because my experiences were far to "real" for me - I wouldn't overcome them, if I just assumed that I was going crazy.

I assumed that I had to be attracting demons. I say "demons", because, from what I've learned, human souls aren't strong enough to manifest themselves in the physical world (if they were then we wouldn't be permanently severed from our bodies after they stop working), though exceptions could be possible. I can't really say - I never died. ;)

Thing is, when I got those scary situations, I focused on turning my fear into anger. Demons are something like us - like our souls - but different. They're mad and menacing, bond in the endless void and wanting to get out of it to somewhere calm and reassuring. To a place, where you can see, hear, touch, smell, taste and lavish in the variety of life. They want to get in here - physically.

They also can get afraid, which means that you can scare them off (Hurayy!).

We, humans, are always afraid of the unknown. Because, if we don't understand how something works than we don't know how safe or unsafe it is and how to defend or simply interact with it. So it's only natural that you might have shat bricks, if a door closed on its own in front of you (I don't say you did, but I remember myself). It's important that, at that moment, you force yourself to turn your fear into anger and direct it towards the entity/entities. Talk with them, give them names, be arrogant towards them, pretend to ignore them or seem unimpressed by what they "do".

If they're nothing serious, they'll just leave you alone after some time.
And closing and opening doors is exactly: "nothing serious".