Switched capacitor sample and hold circuit as as mixer
That's just the math behind that kind of mixer.
To understand that, you should look at the very common example of why a &quot;zero-order hold&quot; is not an appropriate reconstruction filter for DACs. Exactly the same math applies here:
You're producing images of the sampled signal, at regular (sample-interval-spaced) frequency distances. Some of these end up at a lower frequency. With appropriate low-pass filtering, you can build a downconversion mixer from this.
Note that this is, at least as far as I know, a bit of an unusual solution to the mixing problem. I'm not a high-speed semiconductor person, but as far as I can tell from radio applications, up to several GHz, you get better results with actual doubly-balanced mixers, even in MOS technologies; then comes a region where CMOS chopping mixers still work.
I'm sure there's a special application field (maybe together with SAR ADCs?) or CMOS technology where this is advantageous.
Generally, it does have some fundamental problems, as you note:

If the level gets decrease, will it lead to any loss?

yes, means mixing with a decreasing, nonlinear envelope. You get intermodulation within the signal's bandwidth, which is the opposite of what you want.

Out of these three subfigures, which one is correct?

&quot;Correct&quot; for what? This question is inanswerable without knowing what &quot;correct&quot; means. (And I guess knowing that is your homework.)