Today I found that someone (the relation history shows who, but I don’t see the point of typing that out here) has deleted relation 20773 - the international E 45 road across whole Europe! Is there a simple way to get it back without having to create a new relation and readd every segment from southern Italy to northern Finland?
Funny enough I don’t know exactly, but I guess you should be able to upload the same realtion on the same ID again, and it should change status from “deleted/invisible”. You can get the history for that relation by using the API. But I don’t think there is a graphical way to do this, so you need to download the relation then load it into JOSM another editor and upload it.
Side question: I understand that relations are fine for cycle routes etc. following many different streets., but what advantage there is in having E45 as one relation? Doesn’t selecting all highways with int_ref=E45 have the same effect? Are relations good for routing or something?
Well it might seem easier/cleaner to find every way beloning to a relation than every way with int_ref=E45 if you are a database freak.
I think relations are a mistake myself, they are horrible to use.
Think of a highway ref=“B 8” which is also part of a national cycleway ref_cyl=“R 6” and is also part of another cycleway ref_cyl= (Ups! Already in use…) ref_cyl2=“R 8” and perhaps part of an international cycleway ref_cyl_int=“E4711” aso.
Doesn’t it make more sense to use relations for that purpose? 
I think cycle_network=Stockholm;Coastal should work alot better than relation hell.
Your examples are pretty forced imo. The hardest issue to solve is how to have multiple values on on the same tag, highway=residential;cycleway is very common but not supported by mapnik, but then highway=residential + cycleway=track doesn’t render either.
Anyway what makes me sceptical about relations is that they seem to create segments out of ways, and we are back in 2006 again.