Magneto Questions

The moving point and its pivot are probably so worn that the timing goes crazy above 3,000 rpm.

Strobe it and see.

The biggest issue with magnetos is ingress of oil. Your magneto looks to be free of oil.   
From your photos, the first job would be simply to remove the points and polish off the corrosion products. Then recheck the quality of the spark.

Get a proper Lucas manual for the magneto to study before you decide to dismantle it.

To answer your first question, yes the earthing strap is held in between the brass strap at both ends and the carbon brush is held against the head of the bolt holding on the points 

The cable from the handle bar cut out switch then screws into the cover exactly the same way as the spark plug high tension leads 

Looks  like it needs a clean up.  The points and springs look like they were set well initially.... a long time ago.  The build up on the periphery of the points is evenly spread and there is no spanner rash on the various fixings.

Clean up the contact surfaces with fibre strips, test for continuity across the contacts (almost zero ohms), then give it a spin with a plug grounded to the body and see what you get.  If there is no spark, you probably need to go deeper.  If it does, strip it, clean it and set it up with new contacts and a little lubrication then see what you get.
j 

Craig,
magnetos are like the little girl with the little curl. When they are good they are very very good but when they are bad they are HORRID!

If your mag has been rebuilt since say year 2000 and the armeture was sealed with epoxy, you may get away with a good clean.

If it were mine, I'd send it straight to an expert for a full rebuild, Inc rewind, condenser, pick ups and insulators on the bearings. 
Don't even pull it apart, chances are you will break the slip ring maybe even the earth brush.

A bloke in South Australia did mine two years ago for $600 AUD. (about 200 UKP )

A good idea is to get a 'Bright Spark' condenser. Or even get Bright Spark to do the whole job.
Their website is very good.
Don Anson Melbourne 

So when is this little girl with the curl coming round??

Yes there's a small tab on the points to fit into the armature so the points go back in the same alignment from where they were removed 

To use a strobe you will need to accurately determine top dead centre and remove chain case  to mark out the alternator rotor and stator.