I'll answer the last question first... You can already limit how many events/days are shown using the $listDays or $listEvents, or any other of the $list* variables. You can find all the details about them in the Online Docs - Integration - List Mode section.
How to get a single date header in the list... That one is more tricky. There is nothing built-in that will allow for that. I did build a solution which uses the Blog Mode List in a loop to provide that effect, so you can either try to replicate that solution, or use mine which has the bugs all worked out of and provide quite a bit of customization (list past X days, list forward X days, list X days ahead starting X days forward or back, etc). If you are interested in buying my code, use the link in my signature below and I will give you the details.
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* Not affiliated with EasyPHPCalendar or NashTech Inc.