Most likely you just proceed straight to immigration. Which country are you referring to?

What they usually check is:
1. Return ticket
2. Booking accommodation
3. Travel itinerary or a rough plan of what and where you will be going and doing
4. Proof of how you are going to survive the few days/weeks in their country (cash, credit cards, etc.)

Immigration can check all they want, if they suspect you, they may even go through your text messages to see if you are planning to work there or not.

I don't think you'll have a problem but I would say go renew it to be safe.

It's an ETA (electronic). Go to their official website to check.
https://www.eta.immi.gov.au/ETAS3/etas

You should've receive an email on the visa details if you have done it yourself. The email will have the reference number needed.

Then check with the tour agency. I prefer to do it myself even though it's more expensive.

No worries. It's good that you are searching and reading up instead of just asking before doing any digging of your own.

I apply my ETAs directly from the website I posted earlier, which I'm quite sure is the official Aus immigration website. I pay AUD$20 directly on the website using credit card.

Yes there are people who just pay RM20/25 to travel agents and get it done with them. But I'd rather be safe than sorry.