Need help explaining clear differences between these grammar (I know the conjugation, I just need to articulate the distinction).

I’ve been studying Japanese for quite a while but I’m currently trying to put together a compact summary of essential grammar to share and realised I’m still uncertain how to explain just this one in terms of rules.

So the ones I have explanations or some close English equivalent for:

mitai – “is like”

ni mieru – “visibly looks like (lit. I can see that..)”

you – “apparently, seems to be (judgement based on conjecture)”

ppoi – transforms nouns/verbs into -ish adjective

gachi – “has a tendency to be”

Now the problem is these guys: sou, sou da and rashii.

I used Tae Kim’s guide last time and he said that “sou” and “sou da” are two different grammar.

So my understanding is there is one meaning for sou – “looks likely to be” (i.e. a judgment based on one’s observation, e.g. it looks likely to rain).

And the other, “sou da” is for hearsay (e.g. Yamada-san wa sake wo nomanai sou da), and I \*must\* include da or desu.

So firstly, am I correct to say that for hearsay, I \*must\* use (sou da/sou desu), but for observations, I use (sou), for which tacking on a da/desu is for emphasis, and is optional?

Secondly, presuming the above is correct, how do I explain a distinguishable difference between this “hearsay” sou da, and the grammar rashii (which other sites claim also for hearsay, but more “objective”)? Is that accurate and could I have a clear sentence example to drive that home?

Edit:

So the final piece of the answer:

sou da – hearsay but directly from a source without altering the information

rashii – similar to sou da, but for secondhand and unreliable sources + personal perception [transforms phrase into i-adjective clause]