1) no general size, but best is 12 inch in diameter or bigger, info from various forum mentioned the bigger the better, as smaller sized spawning tank produce more female then male.

2) styrofoam cup act as a protective area for the betta to build nest. Without one, he'll get fatigue fast for repairing the fragile nest and tending the fry as during spawning period betta tend to goes into fasting mood, they wont whack anything. they can fast for about a week so just put one in.

3) nothing beat cheap real aquatic plant, get some rm 1 or rm 2 plant. It might produce algea or infusoria needed by young fry. Water lettuce foul the water, better have another jar or tank to culture infusoria with water lettuce.

4) some ketapang leaves and few drop of nika general aid or methylene blue to prevent fungus.

Q1- the setup look ok to me.
Q2- yes u need put a half-cut cup(dont forget to cut a square on top of the semi cup to easy u see got egg or not)
q3- setup everything b4 release the female. so put watever u wanted to put in the tank b4 release the female
q4- put a piece of ketapang leave(optional), take the female out 1st.. wait 1 day only put back like that(provided u had finished setup everything)
*what nicotine said was right too except for smaller tank get more female and i usually dont put any medicine(u need med only when u sick only) but lil bit of aquarium salt.
But i guess a pic explain everything so let me share my spawning tank setup ba