“Yes,” “impossible to say,” and “3rd round”
We can solidly answer your first and third questions.
The second, though, cannot be answered.
“Yes,” you can—must?—choose a third power to manifest
Yes, the second power is still modified by Linked Power, and thus you are allowed—or, perhaps strictly speaking, required—to choose a third power to manifest. Quite simply, nothing says you can’t or don’t do this—and Metapower basically says “you do.”
Of note, Linked Power also basically says “you do”—nothing about Linked Power’s effect is optional once you’ve chosen to use Linked Power (because that would be nonsensical in the usual case). This means that you might be required to choose a third power to manifest here. That’s basically supposed to be the “downside” to Metapower, and if you really want the Metapower’d power twice, but not any third power, you might be forced to pick something—and that might cost you power points.
“Impossible to say,” because we just don’t have enough to go on
In a situation where you have powers, A and B, and you have the Metapower feat choosing A and the Linked Power feat, a chain of A1–A2–B with no augmentation has the total cost of A1 be the base cost of A plus the total cost of A2, with a −2 power point discount, and the total cost of A2 is the base cost of A plus the total cost of B, with the same −2 power point discount. The total cost of A2 definitely includes the −2 discount on B, but then when you add the total cost of A2 for the cost of A1, Metapower is trying to add the same discount again.
Can it do that? The argument for “No” is the single-source rule, which prevents an untyped bonus from any single source from being applied repeatedly to something. There are two possible problems with that argument, though:
Is this really the same calculation? That is, does the discount appear twice in the calculation of A1’s cost, does A1 “see” the discount that A2 got? Or does A1 just “see” A2’s cost, and not how it got there?
Even if A1 does see it, does the single-source rule apply? Are these really “penalties,” or “bonuses” of a sort (even though they’re negative, they’re good things)?
And the answers to both of these are undefined.
“3rd round,” as it’s a round after the Linked Power effect
This part is pretty straightforward: in the A1–A2–B chain, the initial round sees the A1 manifestation, you manifest A with the A2 manifestation delayed a round. And then on that second round, A2 happens, so you manifest A and delay B by another round. B happens the following round.
Has to be said...
Complete Psionic is a pretty awful book. Metapower and Linked Power are part—along with synchronicity, particularly when used with Metapower and Linked Power—of the triad of the most broken material in the book. Synchronicity didn’t come up in this question, but it should definitely be banned—and even with that banned, Linked Power should probably be banned, too. And even then, Metapower is pretty questionable, just on its own.
