I can use Scion of the Ur-Dragon's ability to turn Scion into a copy of another dragon that is in my library. Let's assume that the dragon that I choose isn't a legendary creature. Can I attach Blade of Selves to Scion (which is now a copy of that dragon) and use it until end of turn? I couldn't normally use Blade of Selves on Scion without the Legend Rule kicking in, but now Scion is a copy of a non-legendary creature.
You can target Scion of the Ur-Dragon with Blade of Selves's equip ability as long as it's a "creature you control" (C.R. 702.6a). It doesn't matter whether Scion of the Ur-Dragon is legendary. However, a token you create due to myriad will enter as a copy of whatever Scion of the Ur-Dragon currently is (in terms of its copiable values) (C.R. 706.2, 702.115a). Thus, for example, in general, if Scion of the Ur-Dragon isn't legendary by the time you create that token, that token won't be legendary either. The values copied by the token will remain even after Scion of the Ur-Dragon stops being a copy of the Dragon card (C.R. 611.2a, 702.115a; see also this thread).
Note that the legend rule does not necessarily apply—
if you own a legendary card in your graveyard and control a legendary permanent with the same name on the battlefield, or
if each legendary permanent with a given name is controlled by a different player,
but rather, the legend rule applies only if you control two or more legendary permanents with the same name on the battlefield (C.R. 704.5j).
I can use Scion of the Ur-Dragon's ability to turn Scion into a copy of another dragon that is in my library. Let's assume that the dragon that I choose isn't a legendary creature. Can I attach Blade of Selves to Scion (which is now a copy of that dragon) and use it until end of turn? I couldn't normally use Blade of Selves on Scion without the Legend Rule kicking in, but now Scion is a copy of a non-legendary creature.
Does the Legend Rule still apply?
Note that the legend rule does not necessarily apply—
EDIT (May 17): Edited.