In regards to privacy and blockchain, say I was to purchase a rug from someone in person and was paying with bitcoin. We would need to exchange wallet addresses to make the transaction which would link me to that wallet address. The merchant could then even see my balance correct? I'm having trouble understanding about how to keep your privacy when conducting in person transactions.
He could see your balance of the address you sent the coins from, yes. You should use a new address for every transaction if you're concerned about privacy, but remember bitcoin is a public ledger so all transactions can be linked together. You can use services like bitcoin mixers to jumble your coins to make the source harder to find if you're worried about privacy or people knowing how much money you have in a specific wallet.
I was also questions as to how prices stay stable. With the volatility of bitcoin and all crypto currencies, how does a merchant expect to keep prices stable? If I buy a rug for .00000500 btc, this amount could be worth much more post-transaction leaving me as if I over paid.
You can use merchant services such as bitpay which will give the business owner the cash equivalent straight away to protect against fluctuations. Otherwise, bitcoin always has a risk of volatility so I would treat it as a foreign currency in that respect in as much that you could exchange your Dollars for Euros and then see the exchange rate has shifted either up or down moments later. It's the same with bitcoin, but on a more unstable scale given that it is being used as an asset as well as a medium of exchange. If you choose to accept bitcoin directly without using a service like bitpay volatility and price fluctuations are something you will have to take into consideration, but you can choose whether to hold as a speculative investment or just cash it out asap but that's up to you.