A quote is an estimate, not a promise. It reflects reserves at the block it was evaluated against, and the price can move before your transaction lands. The interface re-quotes every ten seconds, and immediately whenever a reserve-changing event arrives.
What protects you is not the quote but the limit derived from it. Your slippage tolerance sets a minimum output, and that minimum is enforced on-chain by the router at execution — if the price moved beyond it, the transaction reverts rather than filling at a worse rate.
When no direct pool exists between two tokens, the router finds a path through an intermediate asset. Each hop costs a fee and a slice of price impact, so a direct route is preferred whenever one has sufficient depth.
Deadlines matter as much as slippage. A transaction with a distant deadline can sit in the mempool and execute much later, at a price you would not have accepted. The default is twenty minutes.