Does paying above Kaspa's minimum relay fee guarantee my transaction gets mined?

No — meeting the minimum relay fee only gets your transaction accepted into the network's mempool; it does not guarantee a miner will include it in a block. When you submit a transaction to Kaspa, nodes check whether its fee meets the minimum relay fee. If it does, the node adds the transaction to its mempool — a waiting room for unconfirmed transactions — and passes it along to neighboring nodes. But miners operate on a different rule: when there are enough transactions to fill a block, a miner picks the ones paying the highest fees first. If your fee is low and the network is busy, your transaction may wait in the mempool a long time, so setting a competitive fee matters when you need fast confirmation.