I wouldn’t add links to a chain, it can make it weaker. There are different methods of measuring how long the chain needs to be, parktool have a good summary on their website. SRAM’s “big-big+2” always worked for me, but I have a sram drivetrain. Wind the chain around the big chainring and the biggest sprocket, but not through the rear derailleur. See where it overlaps, then count two full links (inner and outer is one) more. If you use a quick link to put it together (I’d recommend that), this counts as an outer.
I don’t know if that method works with the wolf tooth, or if you have to do something special - they might have something on their website?
If you don’t use a quick link, you need to use pins to press into the chain. Sometimes, the original pin can be pushed back in with the chaintool (your Kettennietbrecher), but it doesn’t always work. You can buy new pins designed for this, but its easier to use a quickling and it helps you if you have to take the chain off at any point.