The 2 months are months :)

E.g. if your pass starts on 11 November, the last day of validity will be 10 January. If your pass starts on  11 February, it will be valid until 10 April. The second period is a few days shorter that the first one.

If you have a mobile pass, you can't get a paper version for a certain day. However, all information in the QR code is also available in readable format on the phone screen.

@Nanja, being able to generate a printable PDF (with QR code and all necessary data) for a travel day sounds like a useful idea. Would that be feasible?

It does, rvdborgt. But unfortunately it is not feasible due to fraud/security related reasons. 
@SebastianF, if it happens that the QR code is not working, the train staff should be able to check your ticket in readable format. Although chances are small, if you are forced to pay for a full ticket or a fine, make sure to keep your ticket/receipts and reach out to our Customer Support as soon as possible as they can assist you further.