It doesn't need to but given that the difficulty is ever increasing if you only mine, say, 1/3rd of the time you're at a disadvantage compared to 24/7 miners.

Now if the price of solar electricity is completely free and bitcoin doesn't crash then mathematically there'll come a point when you'll break even but it might take a long while as the mining rewards keep dwindling as difficulty increases while you spend most of your time not mining. Eventually your miner hardware or solar panels will need maintenance and that will increase your costs.

You'd have to do the math to see how long it'll take you to break even, but something tells me that it won't be nearly as competitive as those server farms using cheap hydroelectricity.

Because miners are by far most expensive than electricity, and if you mine at 50% the effective miner's cost is 2x

I think they mean in order to actually make a profit it needs to be running nearly endlessly.