Opening a short position on Kraken requires BTC to begin with? Suppose I have US Dollars on Kraken and no BTC. And suppose I expect the Bitcoin price to drop a bit (which I don't, but suppose) so I would want to speculate and take a short position. 

Is this possible at all, or do I first need to have BTC in my account, in order to 'short sell' them? 

It feels kind of counter-intuitive to first buy BTC to then immediately sell (short) them. 

Suppose I don't want a higher leverage, i.e. I just want to short "1x" so to speak. So the price going down by 7% would mean 7% profit (minus trading fees). Am I right in thinking I should then first buy BTC, and then sell that with 2x leverage?

And similarly if I'd want to short with 3x leverage. But have no BTC yet. Should I then first buy BTC (through a normal order, not margin) and then margin sell it with 4x leverage?
You have to get money into the exchange to purchase and secure your position somehow. BTC is probably an easy way to do it but you could also do it with EUR or USD. You will need BTC to close the position but since you're going to be shorting BTC, you won't want to hold BTC while the position is open, so you'll be holding some form of fiat instead.