2) is just fine, if the shop has been open for a few hours. If it is the end of the day and the shop is closing we might use the simple past, 'Did you have a lot of/many customers today?' If the morning is over you can ask 'Did you have a lot of/many customers this morning?'.If I want to ask my friend whether many customers came to her shop today (let's say it's in the afternoon I'm asking her the question)
Should I say
1) Do you have a lot of customers today?
2) Have there been a lot of customers today?