I am using bitcoin core 0.11.2 on testnet, the blockchain is up-to-date.
1) When calling bitcoin-cli estimatefee I always get -1, what would be the problem?
Not enough data to determine a proper fee yet. Try bitcoin-cli estimatfee 10 and lower the number until you have the least amount of blocks it can give you an estimate for. If 10 isnt enough, you can go all the way down to 25.
btw, where is 2?
4) How does the client currently set the fees? I sent 2 standard transactions and the fees were 0.00001865 & 0.00001125. But most resources say the fee should be 0.0001 BTC per 1k/B. What am I missing here?
The default minrelaytxfee currently is 5000sat/kbyte IIRC.