How can I set a fixed fee sufficient for transaction success in bitcoind? I used to use sendtoaddress with bitcoind and a fixed 0.0001 btc transaction fee in the wallet UI to do the job and every transaction was sent without any problems.

Since version v0.12.0 I can see that the fee is not fixed, plus some transactions don't transmit to the network.

How can I send transaction with bitcoind that will be 100% relayed ?
You can try:

txconfirmtarget=1


If paytxfee is not set, include enough fee so transactions begin confirmation on average within n blocks (default: 6).

So putting it equal to 1 will automatically set the fee to be included in the next block.

Note that this isn't a "fixed amount solution".