Where is it established that the Christian God is omnipotent and omniscient?

Fair question. How’s this?

Omnipotence:
Luke 1:37 For nothing will be impossible with God. (context = the angel appearing to Mary and telling her the plan, and answering her query as to how she’s going to conceive).

Omnipresence:
Galatians 3:28-29 There is no Jew or Greek, slave or free, male or female, for you are all one in Christ Jesus. And if you belong to Christ then you are Abraham’s seed, heirs according to the promise.

I’m sure there are better ones, but those are two that I get from a quick dig.

Well, the Germanic-derived “almighty” and the Latin-derived “omnipotent” are pretty much synonymous: “omni” = “all” and “potent” = “powerful” = “mighty”. The original Greek term is pantokrator, or so sez the International Bible Encyclopedia:

The problem is that, in English, the two words have different meanings. The Germanic word is more common, and thus is not considered as powerful as the Latinic one.

No, I think you’re overstating the difference somewhat. “Omnipotent” and “almighty” are typically presented as synonyms in a thesaurus, for example.

I would agree with you that the connotations of the two words in English are not quite identical: “almighty” suggests something like “really really REALLY mighty” while “omnipotent” implies something more along the lines of “officially certified and guaranteed absolutely ALL-powerful”. But the literal meanings of the two words are essentially the same.

Sure, it could be hyperbolic praise. But is there anything in the Bible that could not have multiple interpretations?

In case it’s not obvious, I am looking for the basis for the belief that God is omnipotent and omniscient. A passage like this one that can readily be interpreted as a clear statement of His omniscience – even though it could also be interpreted otherwise – seems to me like a very reasonable basis for the belief.

In case you haven’t looked yet, Wikipedia does have a page about God’s omnipotence and omniscience. It includes some of the thinkers who’ve contributed to the discussion over the centuries and some of the verses used to support the belief.

It’s worth noting that there’s some quibbling over just what it means to be omnipotent. So, for example, you get the question about whether God can really do anything with every action as an option, or whether he only do anything if it’s within the confines of His nature.

Reminds me of a certain Far Side cartoon.

It would be, if you take the bible to be inerrant, or at least, mostly true regarding supernatural claims. How you’d arrive at those assessments is probably one of life’s great mysteries.