Almost every wallet today uses HD key derivation. You'd need to go back to software from 2016 or earlier to find any that don't. So I'd say your question is moot.
That said, there certainly are signals in on-chain transaction data that let you make informed guesses about what software may have created them, though they're not correlated with HD or not in practical implementations:
Order of transaction inputs and outputs. Some wallets follow BIP69 which specifies sorting the inputs and outputs; other wallets order them randomly.
Types of inputs used: if a transaction is spending a P2WPKH or P2TR UTXO, it was almost certainly created by a segwit resp. taproot wallet (or it was a CoinJoin transaction with another one that does).
Types of outputs used: if a transaction has a P2WPKH or P2TR output, it's almost certainly created by a wallet that supportsBIP173 resp. BIP350 (which specify the address formats for such outputs).
Coin selection: there are many algorithms in used for selecting which UTXOs to spend to fund any given created transaction, including oldest-first, branch-and-bound, single-random-draw, knapsack, ... . Not every wallet implements the same ones, or implements them identically. From the set of inputs a transaction has it may be possible to infer something about which selection algorithm was used this way.
Anti fee-sniping: some wallets timelock their transactions so they can only be included in the current block height or later most of the time, which prevents a 51% attacker which creates a deep reorg from including the transaction there (making it harder for those to get the fee from the transaction).
No. The point of HD wallets is to create a deterministically generated sequence of addresses but which look random and not related to one another. So unless BIP32 is fundamentally broken, you should not be able to distinguish between a HD wallet and a wallet that simply generates addresses at random.
The only way you can know a HD wallet was used is if its owner gives you its extended public (or private) key.