Welcome to the NS Community!
The conditions state that for a non-folding bicycle (even a disassembeled one), a ticket is needed. Also, carry-on luggage should not exceed 85×85×85 cm (so theoretically, a washing machine is allowed).
But if the bike is in a 120×90×25 box or bag, just store it upright against a wall and sit next to it. They will probably allow it.
Just to be safe, you could buy a ticket via https://www.ns.nl/en/travel-information/bikes-on-the-train.html (in August, bicycles are also allowed in peak hours, this for the IC1730 train).
Hi there Niko_cgn and welcome to our Community.
Robert has given the correct answer regarding bicycles in domestic trains.
For the international trains you mention, there's different conditions. You can find more information here. IC 60403 runs as a Nightjet service.