A decentralized exchange or DEX is meant to facilitate the exchange of bitcoin without forcing users to sacrifice privacy or custody to an exchange.
A decentralized ledger is a record of all transactions on a network. This ledger is maintained and updated by many independent nodes, who collaborate based on a ruleset established by the protocol. Bitcoin uses a blockchain and Proof-of-Work to organize the network and maintain its decentralized ledger.
A derivation path is a piece of data which tells a Hierarchical Deterministic (HD) wallet how to derive a specific key within a tree of keys. Derivation paths are used as a Bitcoin standard and were introduced with HD wallets as a part of BIP 32.
The difficulty is a measure of how hard it is to produce a Proof-of-Work, required to publish a block to the blockchain. Bitcoin's difficulty updates periodically so that Bitcoin blocks arrive every 10 minutes, probabilistically.
A double spend occurs when someone is able to spend the same money twice, fooling one or both parties into believing they have been paid. Bitcoin solves the double spend problem through the use of a decentralized ledger and a timestamped blockchain.
If a piece of bitcoin (a UTXO) is small enough, it may cost more in fees to spend it than it is worth. What constitutes dust is determined by the size of the UTXO and the current fee market.
Occasionally, attackers will send tiny fractions of bitcoin (around 500 sats) to random wallets. This is done in order to breach the privacy of those users and drive up the fees they pay.