Does eTA allow me to exit and re-enter Canada?

I'm an exchange student, and I'm staying in Ontario, Canada for a semester (from September to December). I'd like to visit the US by bus and come back, and I'm aware of ESTA (which to me is just the US version of Canada's eTA). I have a couple of questions:

(Most important) Would I be able to exit Canada, visit the US by bus, then come back to Canada, given a valid eTA and a valid ESTA?
My eTA was approved ~5 minutes after my online application. Is this the case for ESTA as well or am I running the risk of not getting my ESTA in time if I apply now (I'd like to travel in ~3 weeks from now)?

Sidenotes:

I've seen this question, but I'm not sure if it would be the same in my case.
I'm a Greek citizen, so AFAIK no special visas are required for me, apart from eTA/ESTA of course.

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Can I come back to Canada with a eTA?

With a valid eTA, you can travel to Canada as often as you want for short stays (normally for up to six months at a time). You do not need an eTA for travel within Canada. An eTA doesn't guarantee entry to Canada. When you arrive, a border services officer will ask to see your passport and other documents.

Does Canada eTA allow multiple entry?

And to answer your question, yes, the Canada ETA grants multiple entries for a period of 5 years after issued or until passport expires.

How many times can I enter Canada with eTA?

Once approved, your eTA is valid for five years or until your passport expires \u2013 whichever comes first. You can come to Canada as many times as you wish as long as your eTA remains valid.

How many times can you travel on eTA?

There is no limit on the number of times you may enter the U.S. under either ESTA of a visa. However, if reentering the U.S. using ESTA soon after staying for nearly 90 days, you can expect to be questioned in detail by the immigration officer about the purpose of your visit.

Do You Need a Visa or eTA to Enter Canada?

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