1) Where can i see my transactions? Any local site? 2)How to do this? 3) How to get free ETH?

1. Mist/ethereum wallet
2. Install geth+truffle and work with it
3. It will immitate mining process and it will be really a lot of ether. Near 5 ether per block (each 13-19 sec)

I dont want to install Mist becouse i have a very small free space on computer

MetaMask maybe?

When u init truffle project and init geth, create your first account - u can run geth with params and then write miner.start() for mining
As I remember, mist and ethereum wallet is opened site of ethereum wallet, which connecting to your local node by port and host, which u wrote in params

Metamask is cool thing too. But I never use it, 'cause on my job mist is smth like standard

So private network - your solution. And then problem of how to connect it is easy for finding solution)