I was grinding and sanding this wooden handle for a day or two lately and I nearly finished it, but I noticed, that I filed off a bit too much at the part, where the axe head goes on. I just took a picture, how does it look and I'm asking for experts now, is it still okay to make a slot for the wedge and it will be hung safe and properly?
With some or most axe and hammer heads you have no choice but to make the top portion of the handle a loose fit at the upper edge because of the 3D shape of the eye. And actually what you have there is not too bad at all.
Rely on the wooden wedge1 and the metal wedge/wedges2 to spread the wood at the top to completely or nearly completely fill the space and create a 'dovetail' shape that will safely lock the head in place and prevent it coming off in use.
If you want to you can leave the handle projecting about 2-3mm (1/8" or so) above the axe head, the projecting wood there is able to spread slightly more than inside the eye and this will add a little extra security.
You might like to look at this previous Answer for a bit more info:
Is it OK to re-use an old iron wedge when handling an axe?
1 The wooden wedge goes back to front.
2 Metal wedges go diagonally or straight across. With 'ring wedges' just pound them straight in along the centreline.
In addition to Graphus' great answer, I would add that the completeness of seat around the base is also important for securing the head. It doesn't need to be perfect but contact should be fairly consistent, symmetrical and as close to complete as possible. If there is enough space where the head doesn't contact the wood, it can give enough mechanical room to slowly (or suddenly) work loose even when wedged properly. A loose head, whether suddenly or over time results in a precipitous increase of dangerous outcomes.
Checking the security of the head of your axe is important before each use. Doubly so with new handles. First, a visual inspection of the seat for any gap between the axe head and it's seat. Then try to wriggle it with your hand followed by some taps on a chunk of wood on all sides, feeling and checking for movement. Deformation of the wood from the impacts of initial use as well as wood movement from further seasoning and normal humidity changes can lead to loosening of the head.
The axe can be a big subject. There are a few basics that can get us far and much of it will come naturally from exploration and experimentation. However, when it comes to the axe, we definately want to learn from the mistakes of others.