Minimum tx amount where amount = fee
There is no minimum amount. You can send 0.00000001 btc and even 0.0 btc without fees and there is a possibility that this transaction would be mined by some miner. But the probability is very low, because "standard nodes" (by bitcoin devs) do not relay such transactions.

You should add a fee if you want to send less than 0.00005xxx (I do not remember the exact value). The fee is 0.0001 per kb for clients running 0.8.x and 0.00001 per kb for clients on version 0.9.x

Here you can see transaction which transfers small amount of btc with a higher fee. https://blockchain.info/ru/tx/b07f23ce5d6a3746a3f8bd5202daa1084686812aa4ecce290208fbe84e68f564