Should a father interfere in his son's private affairs concerning the acquisition of a screen inside the marital home, and can he stipulate that he either encrypt it or leave the house and dissolve the engagement?

The son should not oppose his father's command for something good that benefits him, as obedience to parents is among the most obligatory duties and best acts of drawing near to Allah. The conditions for obeying parents are: that it should not involve disobedience to the Creator, that they have a valid purpose, and that it does not cause harm to the son. Therefore, he must obey his father, and he can try to gently and wisely persuade him that he will not use the means in a forbidden way.