We were actually learning this sugya in my gemara shiur recently.
There is a difference between V’sein Bracha and Ya’aleh V’yavo, in that the former is said during the “middle” supplication portion of the Shemoneh Esrei, while the latter is said as part of the final three brachos (e.g., R’tzei through the end of the tefilla). Thus, for V’sein Bracha, you can make it up through Shomeah Tefilla, but afterwards you must repeat your tefilla. By Ya’aleh V’yavo, you can make it up as long as you have not finished your tefilla. If you finished, then you must repeat.
The Gemara has a discussion clarifying what the end of the tefilla is. It could be at the end of the bracha of Shalom, when you take three steps back, or at the end of your personal supplications if you have a minhag to add them. A further discussion is made regarding supplications before the three steps vs. after the three steps. The last opinion stated holds that customary supplications made before the three steps back (e.g., Elokai n’tzor) are considered part of the tefilla, and thus you can go back to R’tzei and say Ya’aleh V’yavo if you remember during Elokai n’tzor, but once you take three steps back, you have to repeat your Shemoneh Esrei, even if you haven’t said Y’hi Ratzon (the supplication after the three steps) yet. We didn’t discuss this in the shiur, but I would imagine that the above wouldn’t apply to supplications that you don’t normally say, even if you said them before the three steps. I have a recollection that the Artscroll says to repeat if you’ve said Yih’yu L’ratzon (the final sentence of Elokai n’tzor), which would make sense given the above.
One big exception to this is the Ya’aleh V’yavo of ma’ariv on Rosh Chodesh. Here, you don’t go back to R’zei, even if you remember in the very next bracha!
I have not yet learned the answer to the second question (how late can you repeat if you remember later), but since your first tefilla did not “go up”, then I don’t see why you couldn’t say another Shemoneh Esrei if you still have time – as opposed to waiting until the following tefilla, since a tefillah bizmana is better than a “make up” tefilla. I’ll ask a question about it at my next shiur!