Comments Area in the free version of HikaShop

Is there a way to add an area for comments when a customer is making a purchase in the free version of HikaShop?

Also is there a way to have a selection in the shopping cart where they can choose shipping or in person pick-up?

No, that's only possible with custom fields of the table "order" that you can create via the menu Display>Custom fields in the Business edition

You can create manual shipping methods for that via the menu System->Shipping methods and set the option "address override" accordingly for each method.