Both of these are awfully CPU-intensive tasks when not done in dedicated hardware. Absolutely TV signal can't be generated in '51, simply because the TV signal is something far, far away from TTL, modulated waves. But transforming binary signal into TV signal is possible with a handful of analog discretes or a "modulator" like these used in Amiga 500.
The problem is: A 24x60 text display, with 8x8 font is 192* 480 = 92.160 pixels. Times 50/s gives 5.000.000 I/O operations a second. You already see a standard 12MHZ/12 '51 can't create this. Go with 1-bit display, some external hardware and planar gfx (1 byte=8 pixels) and you're down to some 500.000 outputs a second, less trivial though. That hardly leaves any time for normal operation, even with fast derivatives.

As for audio, human can perceive about 24 kHz. For a decent sine wave at that frequency you'd need at least 4 times that, say, 100khz. Every 10 cycles on a /12 derivative.

That means - okay, we can build a '51 based computer with decent audio and readable video. But with one '51 "CPU", one '51 "Video chip", one '51 "audio chip". Another '51 for I/O and interaction with the outside world (peripherial controller) would be really welcome too :) Well, Atari had dedicated chips for all these purposes too!