How to attach horizontal bar to a wooden wall?
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.