How does a wallet decide which utxo to use?

Question

I am using a cold wallet and made a few tx two days ago. However, though what I wanted to send was a very small amount of btc, the wallet made multiple utxo of huge amounts get involved and now all my assets are locked up as the tx are unconfirmed.

Questions;

1. Why does a wallet have to use multiple utxo (input>output 2>2 or 3>2) rather than just use one and split it in two (1>2)? (the aimed tx amount is smaller than each utxo)
2. Is the algorithm to select which utxo specific to each wallet or is there any general rule throughout bitcoin network?

Answer 1

Why does a wallet have to use multiple utxo (input>output 2>2 or 3>2) rather than just use one and split it in two (1>2)? (the aimed tx amount is smaller than each utxo)

There's no generic reason a wallet would have to do that.

Is the algorithm to select which utxo specific to each wallet or is there any general rule throughout bitcoin network?

Specific to each wallet

Answer 2

There are various reason because wallets can use more UTXO's than needed and every wallet has its own policy on automatic coin selection.

In this example, Bitcoin Core do it to reduce fragmentation (to reduce UTXO's with small btc amount): bitcoin-core automatic coin selection

In this example, Electrum do it to better preserve user privacy:
Why does Electrum include seemingly unnecessary inputs in a transaction?

There are multiple goal you may want achieve with a coin selection strategy and there is no one strategy that solves all problems, so if you care on which of your UTXO will be used in a transaction is better to check the transaction before broadcasting it or manually select UTXO's you will use.

If you provide more info on which wallet you used, we can understand what happened in your case.