Sounds pretty similar to me and my grandparents, especially the part about not being vulnerable with each other. Mostly it's surface-level talks. For example, my grandpa is into plants and gardening, so we might talk about the garden or his most recent visit to the garden center or something.
And I'm pretty sure behavior like this is passed down through generations.
Be aware that Koningsdag is celebrated on 26 April this year: if the 27th is a Sunday, it's moved to Saturday.
Public transport should be fine. They will run the holiday service, which might be a bit less than regular service. But especially for bigger cities you should be fine. Expect it to be crowded though.
As for flea markets: I'm not an expert, so can't comment on that.
Edit: this was meant as a reply to OP.