Yes. Anytime you see an article that says "X country runs on 100% renewable" ... it's hydro-electric power every time. So if your country is blessed with a type of geography that makes hydro electric power viable, you're golden!
Solar and Wind cannot power a modern economy without fossil fuel back-up.
Wiki: https://en.wikipedia.org/wiki/Renewable_energy_in_Austria
About your last point: <<Solar and Wind cannot power a modern economy without fossil fuel back-up.>>
I respectfully disagree. I think solar+wind+batteries+nuclear can do the trick. Not everywhere, but many places.
I'm surprised no one talks more about how countries near the equator (DRCongo, Brazil, Malaysia, Indonesia, etc.) will transition to renewables. Wind is much weaker near the equator, and building huge solar farms will mean cutting down precious rainforest. It's a real conundrum!
We use enourmous amounts of energy and we invest enourmous amounts of money in energy production. At the same time we have neglible storage and and neglible investment in storage.
some numbers:
194MWh - capacity of Hornsdale Power Reserve in Australia
161 million A$ - it's cost (https://en.m.wikipedia.org/wiki/Hornsdale_Power_Reserve)
4 700 000 MWh - Australia's daily total consumption of energy of all fuel types (https://www.energy.gov.au/data/energy-consumption)
4700000 / 194 = 24226 - number of same power reserves to store australias power for one day.
24226 * 161 millions = 3.9 trillions of A$ - money needed to build a days capacity in Australia at current price.
(for comparison, Australia GDP is near 2 trillion A$, US GDP is 27 trilion A$)
Conceivable, but a massive undertaking at a scale having inevitable significant problems ($66T price tag for starters).