good questions, Eveningsun. i have sometimes thought about a question which could be added on the list.
3: will the eaglets remember their home nest after they leave it?
i'm afraid that no-one knows answers to these questions for sure.
instead of firm answers i can write down some reflections about these questions. you may then judge for yourself how plausible my thoughts and guesses sound.
i should think that as relatively highly developed animals eagles must have rather good memories. they also live long (if they survive their youth). i think they'll remember what they learn during their lives. the surroundings of their home nest the WTEaglets will learn to know rather well as they don't fly away for good like LSEaglets who fly away for good on the first time. even small migrating birds are known to return to the same nest (box) for breeding year after year so why not bigger long-lived WTEs wouldn't remember and know their nest if they happen to cruise around. - they'll not be welcome there if their parents still occupy the nest.

at the old Saunja nest in 2009 a young 1st-calendar-year eagle once sat on a branch by the nest for a very long time when Linda was brooding. we then suspected that this young eagle could have been Linda's and Sulev's eaglet from the previous year, but of course there was no way to know it for sure.
we have seen in the winter feeding ground and on the seal island that, despite being very territorial, WTEs are also fairly social animals: outside the breeding season they gather in flocks to places where food can be found. i think it is quite possible that for example in winter gatherings eagles might learn to know each other individually so that they'll recognize each other if they happen to meet again later somewhere else. eagles know their own spouse so why not would they be able to recognize also other individuals.
when i watching the winter feeding place i had a few times the feeling that there was a whole eagle family there: a young 1st winter eagle eating while an adult stood nearby and looked at the young eagle eating (a reverse pecking order). in eagle books i have also read about eagle families feeding together in the autumn. so eaglets will learn to know well how their parents so why wouldn't they remember them later?
will it also go the other way round i can't quite even guess. the appearance of young eagles change so radically while they mature that maybe parents will not recognize their offspring after a few years. probably siblings will loose track of each other, too. they are known to fly different ways after leaving their nest. then it might be possible that a sister and a brother could start a family later in their life. this is even more possible if the siblings have hatched in different years. in that case they would have (besides naturally the parents) nothing else in common experience than probably the same nest.