Is the pronunciation of svenska here correct? I learnt it somewhere else as having more of a W sound, like Swenska.
It... doesn't have a W sound per se, but it's certainly not the hard V the western world uses generally. It's a little more liquid: air does not pass between the teeth and lip as hardly as does when you make the English V sound.
If one word ends in an r and the next starts with an s, it's common to merge those into the retroflex rs sound. Whether you do or not depends on your sociolect, mostly. I would never merge here - while e.g. Arnauti would always do.