Thank you, Lauda. Is is possible that transactions will go back to my wallet? (will be dropped from the mempool)
Yes, as answered by the person above me.
It was first time I was sending BTC, I was not aware of the fee rate. I guess MultiBit HD is not very newbie friendly here.
Optimally you'd use a wallet with Coin-control and you'd manually set your fee-rate. You can do that in Bitcoin Core, but that required downloading and verifying the whole blockchain. You can try Electrum if you want an SPV wallet.