If you call putting text together that reads like an assumption, then yes. But it cannot express assumption, as it is not assuming. It is completing text, like OP said.
It's trained to complete text, but it does so by constructing internal circuitry during training. We don't have enough transparency into that circuitry or the human brain's to positively assert that it doesn't assume.
But I'd wager it's there; assuming is not a particularly impressive or computationally intense operation. There's a tendency to bundle all of human consciousness into the definitions of our cognitive components, but I would argue that, eg., a branch predictor is meeting the bar for any sane definition of 'assume'.
Yes, and it can express its assumptions in text.
Ask it to make some assumptions, like about a stack for a programming task, and it will.
Whether or not the mechanism behind it feels like real thinking to you, it can definitely do this.