This somewhat overlaps with Pieter's response:
a. We strongly recommend customers to use CNAME instead of A-record. So in your example: You need to request for a custom URL(www.ourapplication.nl) in the support portal. Then on your DNS www.ourapplication.nl should point to ourapplication.mendix.net using a CNAME-record. If you don't inform us of the custom URL it will not work (you will get HTTP error code 403 forbidden).
b. No, we do not host DNS for customer's domains.
This might be better answered in a support ticket, but... in your specific case... what you did right now, using example.com as an a example instead of your name is:
www.example.com. IN CNAME example.com. example.com. IN A 192.0.2.66
It should be:
www.example.com. IN CNAME example.mendix.net.
where example.mendix.net. is the name you got from Mendix, which points to e.g:
example.mendix.com. IN A 192.0.2.66 example.mendix.com. IN AAAA 2001:db8::31:3024:37:487
Note that the SSL setup you're currently building (as seen in support ticket) is not valid for https://example.com/ so it's no use pointing that to Mendix
If the name ending in .net you got from Mendix is under mendix.net (not mendixcloud.net) the IP-addresses won't likely change without letting you know, so in case you want to build an SSL setup for https://example.com/ you could set A and AAAA (don't forget IPv6!) on example.com, as a CNAME would break your DNS in that case.
Anyway, I'll poke support on monday to get in touch with you and the partner company about resolving this, there's too much open tickets about it now.
I think that it is also allowed to map an A-record to another A-record. Thus you could map your ourapplication.nl domain to ourapplication.mendix.nl.
That way if mendix would ever decide to move their servers your are not afflicted by it.
That being said if you do want to point the A-record of ourapplication.nl domain to the ip you could just ping the ourapplication.mendix.nl application to get the ip and point it to that..