Can I use the the international IC between Dutch cities? I was wondering if I can use this train between Roosendaal and Rotterdam with the standard travel card (OV-chipkaart).
Normal Dutch railway tickets, including the OV-chipkaart, are valid on the IC international train (that goes between Brussels and Amsterdam) within the Netherlands. So in your case you can use the international train between Roosendaal and Rotterdam just like any other train.
I'm not sure what a "standard travel card" is - do you mean an OV-chipkaart?
Yes, you can use any standard ticket (e.g. pay-as-you-go OV chipkaart or disposable ticket from a vending machine) on international Intercity trains (Amsterdam-Brussels and Amsterdam-Berlin). All the usual rules, including discount cards apply. In fact, you will find both of them full of domestic travellers, which can occasionally create some funny interactions (I once witnessed Dutch passengers completely unfamiliar with the very concept of a seat reservation “explain” to German passengers that they could just seat wherever they want).
The only exceptions are Thalys (mandatory seat reservation and no domestic service) and ICE International (rules are more complex).