Yes, stocks can be purchased after the stock market is closed. You can do so by placing an AMO which would be executed the next day once the stock market opens.
The stock market typically runs between 9 in the morning to 3 in the evening. However, after 3, its most likely that the market is preparing for closure where squaring off, and other things are being executed. However, if you want to buy stocks when the market is shut, then you won’t be able to do so.
If you want to buy them, you could place an AMO or After Market Orders that get executed instantly when the market opens up. These orders could range for any segment. For example, it could be for buy stocks, intraday shares, futures, and more. however, do keep in mind that there might be a brokerage fee charged on such orders based on the type of broker used in executing trades in the stock market.
Yes, place an AMO or after-market order. You might be charged a fee based on the broker you choose to place this with.