Yeah, 1mm of lateral-play is semi OK. The sprocket-plate with two bolts may be worn-out or damaged and not sitting in groove of output-shaft tightly. inspect output-shaft's groove to make sure it's not damaged and allowing lateral-play. Groove should have sharp 90-degree edges and corners.
Clicking sound may be worn wheel-bearings. If so, nothing you do with axle-adjusters and chain-tension will fix wobbling and out-of-tension chain. Need to fix wheel bearings first.
Then you can align chain & set tension using this procedure. It's being done on new-gen, but will work on pre-gen just fine.
Link to original page on YouTube.
Also use this string-alignment procedure. Most accurate as it doesn't rely on factory swingarm marks, which may not be spot-on. Also swingarm pivot may not be accurate as well if swingarm is bent or frame is bent. Even with bent frame and swingarm, string method will compensate and ensure both wheels are tracking straight with each other.
https://www.cycleworld.com/2015/12/0...eel-alignment/