1- what is the best wallet?
That's like asking "What is the best vehicle?"
Each wallet is best for it's specific purpose. You'll need to learn what the features and restrictions are on various wallets and then choose for yourself the one that is best for you.
If you don't want to do that, just install Electrum. It's isn't horrible.
2- I have an idea: to make two wallets one for store the amount and one for exchange and play with it and after gain BTC transfer to the safer wallet "first one", is this right idea?
Sure. if that's what you want to do, then that will work fine.
3- what is the fast way to transfer the BTC to US Dollar $$?
Register for an online bitcoin exchange (such as Bitstamp, Coinbase, BitFinex, or whatever exchange you have access to in your country), or find someone near you with localbitcoins.com that will exchange with you.
4- What is the fast way to have this $$$ as a bank note?
If you are using an online exchange, then you can transfer to your bank and use an ATM.
If you are using localbitcoins, then you can just accept bank notes directly from the person you are exchanging with.
5- From my point of view, the mining hardware is the fast, easy and secure way to build BTC's if I want to generate only 20BTC/month what is the cheap hardware I have to obtain to reach this amount?
20 BTC per month?
To do that today you'd need about 253.81 terahash per second.
An AntMiner S7 will generate about 4.73 Th/s, so you'll need about 54 of them. I think they cost about $600 each, so that should cost you about $32400 to purchase.
Then you'll need to pay for the electricity to run them. Each unit will use about 1200 Watts, so if you run all 54 of them continuously you'll use about 47336 kWh of electricity per month.
If your electricity costs you $0.12 per kWh, that will be about $5680 per month in electricity costs.
Keep in mind though two VERY IMPORTANT facts:
- If other people add mining equipment and hash power to the bitcoin network then difficulty will go up and you will get less than 20 BTC per month unless you add more equipment too. (Difficulty re-adjsusts every 2016 blocks)
- In early July, the block subsidy will be cut in half from 25 BTC per block to 12.5 BTC per block. If a lot of people continue to leave their equipment running, then your revenue will be significantly reduced at that time