Hi – great question!
For each event you can set up one or more tickets and restrict the selling window so purchases can be made only within the date range you specify. However, this is not so fine grained that you can narrow the window down to just a few hours (so something like 10 April – 15 April is possible, but10 April – 15 April only between 12pm – 3pm would not be possible without some customization work).
With regards to stock limits – you can set the inventory for each ticket you sell. What you cannot currently do is share inventory across multiple tickets/events.
Does that clarify things at all? Thanks for your interest!