Do miners have an incentive to confirm various transactions from same address? Mempool is really clogged those days. I tried to make a transaction from one of my address to a friend. As we didn't care about confirmation time, I put a 5 sats/bit fee.
2 weeks later, transaction still wasn't confirmed. But, from same address, I had to send another transaction of all remaining funds on the address. I was in a hurry so I put next-block estimate fee.
My second transaction has been confirmed as planned in next block but, interestingly, my first transaction was also confirmed in that block, even if mempool was still clogged.
I want to understand what was the incentive for the miner to confirm my first transaction, and if I can use this mecanism.  For example, if I have to send 2 transactions with confirmation in next block, can I be confident to put high fees in only one of them?
It sounds like you have rediscovered a mechanism called child pays for parent.
Generally, no, two independent transactions could get included in any order even when they were sent from the same wallet or involve the same address.  There is no efficiency benefit to reusing addresses, in fact it has significant downsides especially for privacy.—Miners will simply pick the transactions that maximize the transaction fees collected by their block. In effect, transactions with higher fee rates get prioritized.
However, I don't think the transactions were independent in this case! Usually, when you make a payment from a wallet, the wallet will not have exactly the amount you're trying to pay available in a distinct UTXO. In that case, when you send the payment, the inputs make up more funds than the payment amount and your wallet creates an additional change output to assign the remaining funds to itself. When your second transaction spent the wallet's complete balance, it would have also spent the first transaction's change output. I'm confident that this is how the two transactions became dependent.
When one transaction pays another transaction's output, they can only appear in topological order in the blockchain. Obviously, funds that don't exist cannot be spent. So, when a transaction spends the output of an unconfirmed parent transaction, the child is invalid unless the parent precedes it.
Now, you say that your second transaction paid a large transaction fee. This incentivized the miners to include the child transaction, but to be able to include the child, they first had to include the lower feerate parent. It turns out that the fee bid by the child was sufficient to make the whole transaction chain attractive for inclusion: the child paid for the parent.