Is there a way to see the precise time of when a transaction was sent out? I'm a developer. I'm not really knowledgeable in bitcoin development, yet.
Say, I'm using Electrum wallet. I share an address with someone. The thing is that I need this someone to pay a certain amount of BTC within a certain time-window, 15-30-60 minutes. It's because I have products that are priced in fiat money.
That person will send me BTC. I may open my wallet not right away but in 12-30 hours, to check incoming payments. Or, even if I open it sooner, there may also be delays in BTC network and I won't see a payment, right?
Goal: to prevent a customer from taking a potential advantage of fluctuation of BTC/FIAT prices.
I don't consider handling my payments via 3rd-party crypto-coin payment providers or their APIs.
Is the precise date and time of when a payment was sent attached to a transcaction and can it be retrieved? How, where?
Can it been seen in Electrum?
While Murch answers the technical side of it already, what you're trying to do is simply not possible. There is no provision in Bitcoin to know the exact time a transaction was broadcast (short of running several nodes that connect to enough of the network to attempt to deduce the first broadcast time).
If you're trying to protect yourself against price fluctuations, your best bet would be to have a system that requires a certain number of confirmations within a time window of your choosing (say, 30-60 minutes). If you have not received BTC in that time period, you can cancel the order. If you receive it after the window has closed, you simply refund the BTC back to the customer and ask them to place a new order (or let them use that BTC amount as a credit against their new order).
This ensures that you only have to sell BTC for fiat within a certain window of time, and if the BTC transaction occurs too far after the order is placed, you return the BTC, without touching fiat at all.