You can’t have a backup paper pass, the choice is either one or the other and as you have already bought the mobile version the best advice is to be careful with the security of your phones (and other property) when travelling.
If the DOB is just a digit wrong then it shouldn’t be a big problem.
You can contact Eurail customer services to get help with this https://eurail.zendesk.com/hc/en-001/requests/new?
Just answer your question on multiple destinations with a mobile pass. It has exactly the same range as a paper pass.
@2-of course one cannot change DOB.
There is often a reported prob with those from over the ocean-it sets to CET time-makes 1 day difference, dep. on what time in CA you do it.
BTW_ I am now on day 26 of a 3-month pass and have visited 8 countries now-did not travel every day. Noone till now has asked for ID-so also noone checks birthdate. Nor did anyone ask for it using a 10D in 2M pass last spring.
It is unusual for ID to be checked. The only time this year was in Switzerland on an SBB train where they checked the name on the passport definitely not date of birth.