Changed passport details

There should be no issue with having a different passport number if you can prove you lost the previous one and got a new one. For instance, you could have a copy of the report of your lost passport.

It might not be necessary: For the pass, unless you've already started travelling, you should be able to deactivate it and activate it again with the new passport details.

In general, it's best to only activate the pass shortly before travel, as you never know what might happen and once the validity period starts it can't be deactivated/changed/refunded/etc. 

For seat reservations, I don't think it matters: if the name and date of birth matches, I doubt anyone will notice. And if they do, simply explain the issue.

You will not lose the seat reservations, but you should contact Interrail support and ask them to update the passport details on the pass.

Seat reservations . . . the ticket inspector on the train doesn’t care who made the reservation, what name it’s in, etc . . . so there will be no issue there.

The only place where the passport number appears is in the app.  Some inspectors will ask to see your passport to confirm that the name on the pass in the app (Jessica Branston, for example) matches the name in the passport.  A passport with the name John Doe would be a problem in this case.  A passport with the name Jessica Branston with a different passport number is very unlikely to be a problem.

There may be a tiny, tiny % of inspectors who also check that the passport number on the pass matches the number on the passport, but as above this is easily explainable, especially when you have a new passport showing a validity start date in the last few weeks.