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Does that mean that the relic shouldn’t be on top of the altar like pictured in my OP?
Frankly, yes. That’s the current liturgical norm. Until recently though, it was customary to place relics on the altar.
In the Extraordinary Form, which is still a legitimate form of the Latin Rite, the relics are still placed on the mensa.
If you noticed, at the canonization ceremony yesterday the relics of Saint John XXIII and Saint John Paul II (I typed those names just because I’m overjoyed that I can!) were placed on a special table or stand next to the altar—not the altar itself.
So while relics are not on the altar in the Ordinary Form, they are in the Extraordinary. It’s a minor conflict.

It’s also worth noting that when the Directory was promulgated in 2001, we did not have the same understanding of the Extraordinary Form that we have today, so we can only speculate as to what it might say in regard to this very minor conflict of rubrics. Perhaps the Holy See will update the Directory to reflect* Summorum Pontificum*? Maybe, but I doubt it’s high on their list of priorities.
In your picture, the arrangement followed the Extraordinary Form. Oh well…

I don’t see why it can’t.
As far as the kneeling goes, that’s a custom that dates from time immemorial. If it’s done in private veneration, I see no issue with it.