Drivetrain Dilemma

I had a creaking/clicking sound when climbing. It turned out to be the bladed spokes on the rear wheel where they cross. Some dry lube at each crossover of spokes sorted it out. 

This may not be the problem because these noises are specific BUT: I had a persistent click when pushing hard on the right pedal. I eliminated everything I thought could be related, but Paul Hewitt suggested that noises can come from the band-on front mech. This seemed highly improbable, but I took it off, put some white grease (lithium?) on the band, reassembled and the problem was permanently gone. It's a titanium Merlin and Ultegra 9 speed mech.

I've also had odd noises from the freehub due to pawls being broken or seized. If you can borrow a different wheel from a bike that doesn't have unwanted noises, you my be able to eliminate that.

My money's still on the wobbly cassette though.

Have you tried taking the cassette off and spraying the connecting bolts of any cog groups (ie not the single cog pieces) with some wd40? Spray both sides of the bolt and leave it for a minute to penetrate. Then reassemble the cassette. 

If it clicks when climbing then it might be worth checking the headset is correctly tensioned, and that the stem bolts and saddle clamp bolts are tight.

Could be a missing spacer with the cassette - they shouldn't wobble at all. It's worth checking if it could be the seatpost, so just loosen it, move it a bit and put it back where it was and tighten up again though if it's carbon then it's worth removing it completely and putting a bit of carbon assembly paste on it (which can help prevent it seizing).

I've solved a clicking bottom bracket previously by using a bit of loctite on it to "stick" it in place, but that was a pressfit so I'm not sure if the same applies to yours. Double check that the chainring bolts are all tight too as that can cause clicking if you've got a slightly loose one.

Some movement is fine with jockey wheels, but make sure the plates are properly fastened as they shouldn't have any movement.

Chainring looks fine to me and they should last for ages as long as you replace chains regularly.

I had a clicking on uphill - turned out the cassette was slightly loose.
Others have found it was the seat post.
Often said that the noise is transmitted around the bike so finding the source is tricky.

You have to reply (to yourself) to attach an image.

I'd be a no to replacing the chainring you pictured.  But keep an eye on your chain wear.
You may not have the right spacer behind your rear cassette - it should lock down solid with no chatter, as you say. Jockey wheels wiggle a bit - they're only plastic on a metal bushing or bolt, not much to go wrong. 
drive train clicks under load are one of the great cycling mysteries - the only b/b variable is the l/h crank - is that fully on, with the plastic bolt done up and the fixing two bolts alternately torqued up? The problem is probably arising from some other part of the drive train, so for example Is the derailleur hanger true?