What effects are used here

Around 0:22, the male part.

Close mic’d studio recording - just a touch of room reverb.

Can I do this with a Rode video mic, no studio and artificially adding the room reverb? If so how?

That’s not really the right sort of mic for using close up. A “large diaphragm condenser” mic is what I’d go for, but if you only have one mic available, then give it a go and see what you can get.

If you are not in a studio there will probably be enough (or too much) natural room reverb, so you are unlikely to need to add a reverb effect. The example recording (Around 0:22, the male part) is pretty “dry” (very little effects of any kind).