IMO when you buy used the buyer has to be aware and not depend on the seller's wishfull thinking. The machine could be on it's last leg or the seller use to getting it started and it operation. (crap viberating loose which may require periodic tighting???)

Snow blowers vibrate alot especially older worn ones, so close inspection before use looking for loose hardware is must. As for the carb. cold (like when snow on the ground)starts are easy to flood and engine. maybe revist you starting technique??. Problem with engines setting for long peorids of them are carb. problems due to stale fuel plugging fine ports and causing floats to stick.

some times we get good deal on used and sometimes we got work to do.

I don't think the auger bearing needs to be pressed. The bearing should be held in place by a retainer on the auger housing and the shaft should slide right through.

I agree with Bay , the bearing should be retained within a pillow block retainer secured to the blower / auger housing . Some xtra hands sometimes helps with the aligning and securing .