txbanditrydr basically had all of your answers
A couple of things on your chain adjustment.
1. Firstly, (likey goes without saying) remember you have to loosen the axle to adjust the chain.
2. It is common for the brake side adjuster to feel loose when you back it off. You normally have to tap the axle forward to tighten it up. (Or give the rear tire a good "boot" from the back)
3. One way to verify that the wheel is straight is to measure from the centre of the swingarm bolt to the centre of the axle.
4. Make sure you measure the chain tension on the "tightest spot" and still have sufficient free play. A chain with 6000 miles on it will likely have at least some wear. As you rotate the wheel when the bike is on the centre stand, you will feel tighter and looser areas on the chain.
5. Remeber to clean, lube and ensure everything is tight.