Rio de Janeiro 10 days in august 2014 many questions !

Either bring some cash in reais for a regular yellow taxi (and find an ATM inside a bank for further cash needs) or use a credit card for the pre-paid taxis for which you will be solicited as you make your way through the arrival burro-crazy. Up to you if it's worth 40% more.
Visa and MasterCard are widely accepted,but don't let the cards out of your sight during processing.

As for tours, Grayline spends a lot of time picking up and dropping off at various hotels. A waste of time, IMO.
There is no hop on/off bus.
Private guides are expensive, especially solo.
The common sights can be seen by taking a taxi to and from. Maybe see if someone on Couchsurfing is willing to accompany you for part of the time until you feel more comfortable. Or get a private room in a hostel and meet some fellow travelers.
Most?Many? here are not enamored of the idea of favela tours, afaik, so you may not get much support/help here on that.
It might be a bit cool for the beach.

Use your credit card for the prepaid taxi you can get inside the terminal. And don't carry cash; use the ATM's and just watch what is going on around you while you do that. Carrying a lot of cash is much more risky.

And you could do everything on your wish list in 4-5 days. 10 days would be a for for Rio. If I had that much time, I'd plan a bus trip south to Angra dos Reis, and take the ferry out to Isla Grande.

There are cambios that are open at that time and will still be by the time you get through immigration and customs. If you haven't brought reais with you then you can exchange euros or dollars there.

http://www.infraero.gov.br/index.php/aeroportos/rio-de-janeiro/aeroporto-internacional-do-rio-de-janeiro/facilidades.html

Taxis taken from the curb are quite safe and are also considerably cheaper than a radio taxi, which credit card function aside offers no tangible benefit. Once you are in town you can go to any ATM that will accept your card. Banco do Brasil, HSBC, Citibank and Bradesco all take foreign cards. It's usually a good idea to use an ATM inside a bank where possible, it reduces but does not remove the risk of having your card cloned or skimmed.

All of the sites you have nominated are standard tourist sites and security really isn't a major issue. Even the Santa Marta favela can be done on your own. You can take a cab to Botafogo for a few reais and then take the plano inclindao up, if you want your photo opportunity with the statue of the late kiddy fiddler ad king of pop, Michael Jackson. To be honest it's not a huge walk from Botafogo metro station, you can walk there in about 15 minutes.

Apparently the expression ki**y -fiddler ( in reference to the statue of Michael Jackson) is still verboten on here. Just as well I didn't mention Jimmy S**ille

Apparently the moderator is still cogitating on what was a quite inoffensive post.

When you get there ask for the free tourist map from your hotel. It has all the buses on it. When you get on the bus tell them where you are going (have your guidebook with the Portugese names if you don't speak the language) and the drivers were great with me, stopping and letting me off. I spent three weeks travelling solo and did a lot of it by public transport. I used public transport but I arrived earlier than you. I used the bus loads - but keep your change handy! It was very easy by letting others on first and watching what they did. I didn't go out on my own at night because I was in Lapa. If budgeting is a factor then check out the offers by hostels which you'll find around - they have organised tours which are the same as those offered by expensive hotels but a lot cheaper!

We found ATMs in Brazil often didn't work for foreign cards. As you're travelling alone, I suggest to bring some cash euros (liek 100 or 200) as a backup, with the idea of not spending it but just having it as a backup.

10 days in Rio, jealous of that.