but somehow I never manage to make the chain go both on the smallest and the largest gear.
That sounds like a slighly bent hanger indeed. Either that or the b screw (the one that sets the tension). It's fairly easy to bend a hanger; the other day mine bent after a fall.
I got my alignment tool from Aliexpress. Quality is amazing! To be honest, it's on pair with Park Tools.
It might be worth a try. For now I had brought it to a repair shop to fix it.
I also often buy tools at the Decathlon.
They also have good tools for a reasonable price. I don't know if that is a worldwide firm. I know it is in a lot of European countries.
Decathlon, yeah, they have some nice deals. Bikeinn as well. Have you ever tried that? In Europe there's also Chain Reaction.
I don't know BikeInn and Chain reaction.
I also sometimes buy online at Mantel.com
Those are huge chains. I only bought a pair of tires from Bikeinn. My favorite is Aliexpress though -- there's a bunch of low 1uality stuff and knoc-offs there, but the good stuff is generally superb