I want to set the horizontal bar on the wooden wall above the doorway.The wall thickness is 16 cm., 2 cm layer of plaster. What is the best and more reliable way to do this? Should I attach it over the plaster?
Wooden wall? Pretty rare that walls are made of wood. Are you talking about the molding around the doorway?
The following diagram shows a typical way that a door might be framed:
Every door is a little different, so you need to determine how your door is framed. Your goal is to get the provided lag bolts to go at least 3.5 cm into solid wood. (I would not use those anchors unless you were fastening the bar to a brick or concrete wall.)
In all probability it will be impossible to get the bolts deep enough into solid wood because the spacing of the framing elements will not match your bolt holes. Also, the molding on the door may interfere with the mounting.
So, to get your bar right where you want it, you will need to add a mounting header, which is a thick board (or two thin boards) which is attached to the wall, and then the bar is screwed into that board. Your mounting header should ideally be between 5 and 6 cm thick.
Generally, what you have to do is make exploratory drill holes to discover where the door's framing members are. Once you know that, you can plan to cut and attach your mounting header appropriately. To attach your mounting header, you will need long lag bolts because they have to go through the header, through the plaster and any lathe and then deeply into the framing member. So, your lag bolts need to be 10-12 cm long and should have washers.
I should mention that normally, at least in the US, chinup bars of that type are designed with bolt holes 16 inches apart so that they will mate with wall studs which are normally spaced at that distance. The bar is intended to be mounted to a wall, not above a door.
Some of this is a repeat of Tyler's post, but I just wanted to start from scratch and explain my take on it...
The spacing of the supports for the bar will most likely fall in places where there is no framing. It would be a rare coincidence if it does.
If you are going to use this as a pull up bar for exercise, you will need to install a large enough piece of wood over the door first to attach to all the available framing in the wall, then attach the pull up bar to that. The wood that you apply to the wall should be thick enough to allow the screws that hold the pull up bar.
It looks like the screws are scheduled to go into framing about 50 mm. Here is how I figure that, 70 mm lag screw-15 to 20 mm for finish wall, 5 mm or so for the metal mount. The plastic wall insert is most likely for a concrete wall, which would be your best bet. About mounting it on plaster, it will crumble the plaster. Don't do it.
Here is how I would do it since I would not want a 50 mm thick piece wood secured over the head of my door. Besides wood that thick is not readily available off the shelf in the States. I would get a section of 2"X10"(40X250) or 2"X12' (40X300), depending on the spacing is from upper to lower mounting holes. Make sure the wood is 2 to 3" wider than the spacing is tall. Also make the legth of the wood a few inches bigger on each side of the mounting holes, if that dimension is at least the width of the door trim. If it is not the width of the door trim, make it the door trim width. and center the bar on that.
Drill through the mounting holes into the wood all the way through and hold the bar in place with washered bolts recessed into the back enough so the bolt head with the washer is not beyond the surface of the wood.
Locate all the framing in the wall over the door and with washered lag bolts 4 1/2" (120 mm) like the one you have in the picture, but with a washer on it as well, set those through the wood in groups of 3 lags each. The top and bottom lags about 1" from the top and bottom, and the third lag in the center of them. Tyler's drawing of the framing in a wall is accurate, the objective is to get the screws into the king studs, they are the strongest part of framing around the door. If you could find that the top plate is possible to screw into, that would hold so much better.