Credit cards are backed by loans which are typically broken into subaccounts to allow the issuing bank to treat different portions of your balance differently. Besides allowing for management of promotional balances, this is important for other basic functions where the bank needs to break down balances into different categories, such as grace periods for new purchases, etc. It also allows the bank to track different balances for cash advances (which usually carry higher interest rates and/or additional fees), balance transfers, and normal purchases.
So, essentially, behind the scenes, your credit card is split into buckets. That big purchase you made during the promo period goes into a bucket of "promo period balance" and the other purchase(s) you make go into a different bucket of "normal purchase balance." When your card cycles each month, the calculations for things like fees, interest, etc are essentially done separately for each bucket of balance. So, the bank will calculate interest for your regular purchases separately from your promo purchases. Typically, in a credit card statement, the balances will be broken out into these buckets in some fashion on your statement, usually in the totals section at the bottom after the transaction details.
The bullets at the end of your question raise an important point - when you make payments, which balance(s) do those payments apply towards?
When your card cycles, a minimum payment will be calculated. The minimum payment is made up of all the interest you owe at that point, plus a (painfully low) portion of your total balance. If the payment you make is equal to that minimum, the interest is satisfied, and the portion of the payment allocated to balance is applied to whichever bucket the bank wants. So, if your minimum results in $100 of interest and $10 in principal, that $10 can be applied arbitrarily by the bank - different banks have different rules, so if you want to know where it will apply, you should ask your bank to explain their rules.
If you make a payment larger than the minimum monthly payment, regulation requires that the bank apply the additional principal to the bucket with the highest interest. This helps consumers, because it will reduce the interest you owe the quickest.
There is an exception to that rule which may be relevant to your example, and depends on the type of promo. Many introductory "zero interest" promos are actually deferred interest promos, not true zero interest. A deferred interest promo means that if you exceed a certain timeframe for paying back that promo balance (say, a year) you get a sudden hit of the entire interest against that balance. If you have a deferred interest promo, the bank must apply excess to the promo balance first for the two cycles immediately before the promo ends. This is to protect people from taking a big hit of interest because their payments were being applied to normal purchases instead of the effectively zero balance promo purchases.
As a reference, the regulations around credit cards changed significantly in 2009 due to the Credit CARD act, which is available on the ftc website if you want some light reading material.
