Can someone please describe how the singlename option market opening process works? I often see some markets open many minutes later like 9:35-9:40. Thanks.
The answer is not that simple. There are 16 US option exchanges. Each has their own opening process. But to make a short answer, most of them wait for the underlying to open before triggering the opening of the corresponding option. And to identify the opening of the underlying, they wait for the first trade. Some exchange may configure some options to open automatically at a pre-set time. There are exceptions on some strikes where there are unbalances on the order book (ex.: buy mkt order without any sell order). To really know the details on how each option exchange deal with their respective opening, you must read the trading rule for each exchange.
Here is how it is handled on the CBOE owned exchanges. Warning, lots of information. US Options Opening Process (cboe.com)