difficult to understand but it is so, right?
not really difficult to understand and yes you are correct.
Will I be forced to pay the salary tax even if there will be a lower salary cap in the new series (where I will have the game's income)?
there is no salary cap. What you are probably referring to is your own personal economy being in the red and you forking out overextension tax on top. Overextension is charged as a percentage of that negative balance (after the balance has been reduced by the training exemption - I have had over 400k training exemption before and I'm sure homegrown teams have gone higher).
I believe overextension tax is not charged in the first week (maybe 2 if you don't have a home game?) of the season otherwise many promoting teams would pay it for no fault of their own. Demoting teams only benefit in this specific instance, as their TV money in the first week is based on the higher division amount.
Just make sure you pay salaries your gate receipts allow you to, while staying profitable and you'll have no problem.