Carnaval 2016 runs Thursday February 4 through Tuesday February 9.
The big nights in the Sambodromo in Rio are Sunday (7) and Monday (8) when the top samba schools parade.
Your stay will probably be governed by the dates of the multi-night packages hotels sell. You should be booking now, before choices diminish. Plan the rest of the trip around these package dates.
Tourists usually stay in the beach neighborhoods of the Zona Sul (Copacabana, Arpoador, Ipanema, a Leblon), but neighborhoods like Gloria, Botafogo, Flamengo, Laranjeiras, etc are also OK. If you are near a metro stop, you can reach the Sambodromo by metro.
There will be blocos (block parties/parades, large and small) in the neighborhoods. The schedule comes out later.
For other sights to see, read the informational site
www.ipanema.com and perhaps the online version of Rio for Partiers (despite the annoying name). Tourist sights will be very crowded.
These ticket agencies have been around for a long time:
Rio-Carnival.net
Carnival bookers
Carnivalservice
You will read online complaints about the delivery system, which gets overwhelmed occasionally and breaks down, but overall service is OK.
The sites have good info about how Carnaval functions, and Sambodromo locations.
Generally, you want to be in the middle sectors of the grandstand, with views of the parade in both directions. (Make sure you look at an updated map. The even side was rebuilt a couple of years ago.) Sector 9 grandstand is the only one with reserved seats, is mostly foreigners (not as spirited as other sections), and is the most expensive. Sector 11 is next to the "musicians' niche" where they march in and stay, playing, for most of their school's parade. There is also seating at ground level, a totally different perspective, at reserved tables/seats.
(If there are questions I, or the ticket sales sites, haven't answered, let me know.)
For the falls, you probably want three days, two nights, including travel in and out. The Brazilian side of the park takes about 3 hours to walk and take photos, and the wonderful Bird Park near the entrance, another 2-3. The Argentine side of the park has more trails, mainly the Upper and Lower. Make sure you have paid your Argentine reciprocity fee online and have the receipt. Do take a boat ride under the falls (from either side). You can get around by local public bus or by taxi. I would stay on the side you are flying out of, in Foz do Iguacu or one of the more resorty hotels along the road to the park entrance. Staying in the park is possible (at Belmond Cataratas), but expensive and IMO isolated (from food and nightlife options in town).
You may not really have enough time on either end to do the Amazon, which will take a full day of travel to Manaus, most of another to get far enough out of this huge city to make a less than superficial jungle experience, the tour days, and then out again.
The Pantanal is better for wildlife viewing, so you may want to do some research into that side trip.