This is somewhat speculative, but if you look carefully at the video of the speech, he appears to go on a little improv and not actually be reading from the glass teleprompters (located the sides) when he gave the exchange rate. So I think we can mostly exclude that he might have had a bad speech writer on that specific issue.
And it appears that the 200 roubles/USD is a repetition of an older line of Biden. According to the NY Post, he said exactly the same thing on March 11, "to a conference of House Democrats in Philadelphia". The rouble was lower then, but arguably not that low, at least on the official markets (114 in Moscow, 125/135 on Refinitiv. It had also hit an intraday low of 132 even in Mosow, on the day before.)
It's worth recalling that the White House has been forced to issue some level of corrections lately to Biden's unscripted remarks, most notably on Putin being a war criminal and to "cannot remain in power". The latter remark appears to have been delivered in the same speech in Poland as the most recent 200 exchange rate claim, by the way. I guess the exaggerated exchange rate didn't elicit enough pushback or questions from the press (or for Moscow), for the White House to correct Biden on that talking point (now or on March 11).
As for the future predictions on the Russian economy... Well, Biden wasn't exactly precise on the time frame. If sanctions stay in place 50 years like for North Korea or Cuba... who knows. But yeah, that's an extreme scenario. That technique is pretty common in politician's speeches, by the way: present some extreme future scenario without caveats. You'll note that Putin does the latter too, e.g. claim NATO is going to put hypersonic missiles in Ukraine, or that Ukraine was going to acquire nuclear weapons with Western help. All predicted to happen at some rather unspecified point in the future.
And some sources like IFW Kiel put Russia's GPD growth at about -10% per year, long term following a decoupling of sort from the West. If that were true, it would take only 7-8 years for a 50% drop from the current GDP. N.B. that model "simulates a doubling of non-tariff trade barriers, but does not model the recently adopted sanctions against Russia."