There is a thing that i dont understand... If i measure winding resistance of the transformer primary winding - will result depend if secondary is shorted or open? If yes - why? I also attach the sheet from a book.
If you measure the primary winding resistance using DC then no, the state of the secondary does not have an effect. If, on the other hand you measure using AC then certainly, the secondary plays a role and the impedance seen at the primary contains primary impedance and referred secondary impedance.
Your book figure shows AC applied with secondary shorted will be the total winding resistance. With secondary it will open will be primary only.
To measure resistance on AC only the real component of current must be extracted, which is a small percentage of the reactive impedance. It is measured at some ~10%V such that current <=10% of rated current to prevent over heating often calibrated at 75'C or 85'C. Some rack mounted industrial instruments use a 10A constant current source for large XFMR's.
A DMM might use a 0.1mA or 1mA pulse integration method or a CC DC method which has error with Ic=LdI/dt until the core is saturated. An RLC meter may use 60Hz , 1kHz, 100kHz , and maybe 1MHz constant current source (CC)to measure impedance and separate R,L(f),Q results.
If saturating a transformer say with a LiPo cell dI/dt=V/L and then it rises rapidly to saturation and when constant will give the DCR or DC winding resistance. However the core will have energy stored and ought to be demagnetized with half the saturation time in the opposite polarity assuming it was neutral to begin with. Otherwise a variac is used to swing slowly up to max. and down to zero.
example of part 1 of DC method for primary or secondary only show I in Amps vs time in seconds for a large core with saturation beginning at 25s and ending at 50s.