Learn English – Which is more correct: “embodied by” or “embodied within”

I have been using the following phrases but I am still not confident that they are grammatically correct and sound right:

"in regards with something"

"in regard to" is the right way here.

"with regards to something"

This is OK. Somehow I have the feeling that "with regard to" is more normal though. Paul Brians seems to back this up.

"regarding something"

This is OK, e.g. film title "Regarding Henry", etc.

I have also heard/read people using an arbitrary combination of the above (e.g. "in regards to"). Are those correct? If yes - are they equivalent or the usage depends on context?

It's much easier to answer your question if you put in some examples you've seen. Anyway I hope the above is enough.

Note that there is a completely different usage "regards to" as in "give my regards to old Broadway and tell them I will soon be there" etc.

There is absolutely nothing wrong with

Since it's raining, wouldn't it be a good idea to bring an umbrella?

Look at a few other constructions to see how natural it is:

Since you're going to the store anyway, wouldn't you like to pick us up some ice cream?

Since our success is uncertain, wouldn't we be well advised to consider how to minimize our risks in case of a downturn?

The first clause assumes a fact, and the second balances it with a speculative counterpoint. That is grammatical, unexceptionable and, incidentally, one way to make a sentence interesting.