If the declared card is a monster card? can you set it on the field, same thing to setting the declared spells or traps on the field?

no because they cant be played like the pieces of destiny board with out it on the field.

What about for those cards already set on the field, can you flip it?

Prohibition
PSV-039
Continuous Magic/Spell
When you play this card, declare the name of 1 card. As long as this card remains on the field, the declared card cannot be played. The cards which are already on the field before this card's activation are excluded.