Arriving from where? IMO, if arriving and departing from Brazil, there is no reason to stay in Argentina. Stay on the side you will fly out of, to avoid any slowdowns at the border at a crucial time. (The IGU airport is close to the park entrance btw.)
It is a simple local bus trip to the other side of the park. It does not take very long. Take a taxi for more comfort, speed..... and expense. .
The Argentine side has 3 paths; you can do any or all. Some advise getting there early and taking the train to Devil's Throat first thing to beat the crowds. I stayed half a day and used the other half for a boat ride under the falls. You could also take a swim suit and take a dip in one of the popular rivulets in the shade of that side.(It's likely to be very hot and humid.)
I also do not think there is much advantage in staying at the Belmond within the park, where you are dependent on a taxi to eat at other than the hotel restaurant. The Brazilian side of the park has one path and it can be walked in about 2-3 hours, with plenty of time for photos.
IMO the Bird Park is well worth seeing. It is very close to the entrance to the Brazilian side of the park. It takes about 2-3 hours to see, lingering a bit.
In addition to the Belmond, there are lots of resort style lodgings on the road from the park to the town, as well as many in the actual town of Foz, where most restaurants are also located.
Just take a taxi to the dam. Any hotel can arrange for one or simply step onto the street and hail one. Check the tour schedule for the dam itself.
There are boat rides under the falls from both sides. Macuco Safari is the one in Brazil. It's Gran Aventura in Argentina. You will get very wet, so bring a change of clothing.