UTXO Model and Trans Fee / Kb Clarification
does my wallet remember that these 2 btc came from separate UTXO's? Or does it &quot;get melted&quot; as someone alluded to in my first link. More precisely, if I send these 2 btc to Gerald, will it show 1 input or 2?

(1) Your have a single 2 BTC UTXO, created by Alice's transaction. That transaction spent two UTXOs, but melded them into a single one. Your wallet doesn't care about its history - it has one UTXO, and when spending it, it needs a transaction with one input.
It is possible for wallet or other software to figure out the history of the coins, and figure out that it came from a transaction that spent two. But it has no impact on future transactions with it.

Does this mean she now has 3 inputs and 2 outputs contributing to the size of the transaction (and thus contributing to the size of the fee)

That's right. You'd create a transaction with 3 inputs (each 1 BTC) and 2 outputs (one of 2 BTC, one of 0.5 BTC). The difference is 0.5 BTC going to fees.

Do they typically do this in a most efficient way?

Often, no, actually. Because &quot;most efficient&quot; isn't the only criterion to optimize for. For example, you want to minimize the cost of transactions now, but you also don't want to bring your wallet in a state that increases the cost of transactions later. For example, some strategies for coin selection (as this problem is called) would result in continuously grinding down your coins into ever-smaller change in typical workloads, making it more and more expensive to send out future coins.
Some wallets will take current fee conditions into account to make these decisions.
Overall there is a significant amount of work analyzing various coin selection schemes. Some are featured in Mark Erhardt's master thesis.