fmcw radar sampling requirements
A quick scribble on paper shows that FMCW radar has a resolution of 

$$
\Delta d = \frac{c}{2b}
$$ with $c$ being the speed of wave propagation (aka speed of light, essentially), $b$ being the bandwidth, and $2$ coming into play because the wave has to trave both ways. For your $\Delta d\overset != 1\mathrm m$, 

$$
1\mathrm{m} = \frac{3 \cdot 10^8 \frac{\mathrm{m}}{\mathrm{s}}}{2b}
$$ 

which means you'd only need $b\ge 150\, \mathrm{MHz}$ in my calculation.

That's something that software defined radio devices can do nowadays.

Hence, to answer your questions:
My questions:


  How, if at all, high-resolution, high-bandwidth digital radars are realised in practice?


Simply be mixing the signal down to baseband (or a low IF), and then sampling it with an ADC.


  what would make sense in case of FMCW radar is to mix the transmitted signal and the target return signal and digitize only the beat frequency for Inverse FFT and further analysis.


Yes, that's the way it's done in most "small" FMCW radars, for example automotive radars.


  In that case, could you still call it a digital or software defined radar?


Puh. Digital: yes.
Software defined: well, if everyone asked me, no, but paper doesn't blush, so there's probably someone out there who calls this kind of radar "software defined". Please don't do that.