How long has she been sat? Mine is a bit older (1972) but had little use for the previous 10 years when I bought her 18 months ago. She was really stiff and bouncey to begin with and it took a good couple of 1000 miles to loosen up - like most classics they don't like to be sat. I would certainly recommend getting some lube in the rear springs. Just replaced mine and its make an enormous difference to the ride quality. Stiff rear suspension can also cause the steering/bonnet bounce.
As said above - check tyre pressures. I run mine on the high side at 22psi, but I have larger tyres than standard and want to make the steering a little lighter. I find the steering quite direct and haven't noticed an issue like you've mentioned so not a 'they all do that' thing.
If it's a new exhaust, are you sure it's just not 'new exhaust' smell and all the storage coatings burning off?
Again, never noticed a smell with mine, and I rarely have the side screens on, so it's definitely not a case of 'they all do that'. If it does continue, you could always consider a side exit. I made one for mine for under £60.
