Mac mini incompatibility with HDMI to VGA

Solution 1:

I understood is that from HDMI to VGA, it does not send a signal since it is analog and it does not work.

No. HDMI sends a signal, but as you've already noted, one is digital and the other is analog. The signal is there, but it may not be sufficient enough to be detected.

My question is could I go from HDMI to DVI, then from DVI to VGA; would it work?

No, I don't advise this at all (note: it may "work," but it won't be reliable). A general rule is more conversions = more points of failure. You are better off making a single conversion: HDMI → VGA. Less complexity = better reliability.

Your best bet is to get an active HDMI to VGA adapter.

The key to getting a reliable signal is using an active adapter. (The above link described a similar question regarding a Mac mini as well). The difference between an active and a passive adapter is that the former recreates the actual signal whereas the latter only "reorganizes" the pins outs.