Can one node receive two transactions from the same user (doublespend)?
No that would not be valid, the node would reject the second transaction it saw, because it would know the UTXO was already spent by the first one. If a miner tries to include both in a block, that block would be invalid too for the same reason. 

The exception is if the first transaction signalled to opt in to Replace-by-fee and the second transaction had a high enough fee to replace the first one. (BIP 125)