Word order in: "We from equation (A) obtain (B)." or "We due to a+b=c find that (C) holds."

You should write these as:

From equation (A), we obtain (B),
Due to a+b=c, we find that (C) holds.

The subject doesn't have to come first in English sentences, and these are more natural word orders than the ones you suggest. (And we as a subject is so innocuous and unassuming that there's no reason that you need to contort the more natural word order to put it first.)

I believe your suggestions:

We from equation (A) obtain (B),
We due to a+b=c find that (C) holds.

would actually be classified as grammatical, but their word orders are rather unnatural, so unless you have a very good reason for putting a adverbial phrase between the subject and the verb, you should avoid it.