All language and dialect has a knock on effect on all other statements.

What?

You're saying that if I go to Liverpool and pick up some scouse words, that has some effect on the meaning of everything else I say?

That doesn't sound right.

If I can convince you to use a set of words incorrectly, or use faulty logic sets

Those are two very different things. Using faulty logic is a thinking blunder, that will be corrected when it's pointed out or it's a symptom of a mental disorder such as schizophrenia. Using words incorrectly is nothing of the sort. It might lead to miscommunication, that again, generally can be resolved once you've worked out that you're not using the word exactly the same was as the people you're talking to, but it's not related to thinking the world is flat.

I can use these as tools, to shift logic across unrelated topics.

What tools?

Say I redefined God, then I can convince you that God exists.

Not really. If you defined god as the keyboard I'm using now, then you could convince me that that exists. But that's not convincing me that god exists. It's just the keyboard that exists.

Then at a later time, I change the definition of God back to how I see it.

When you do that, I no longer accept that god exists. Because by redefining a word, you don't change my core beliefs, just the words you're using to describe them.

I have now manufactured your consent, and you now believe in my God.

That's not how believing things works.