No problems like that on mine - at all.....ever
Is yours modified in any way? Non-standard tyres? Wheels? Suspension? Not that you shouldn'r or couldn't modify any of these items, but just interested......
Oil dripping onto a "transmission connecting point"??????? What????? Sounds like you need to go to a dealer who doesn't talk rubbish.... and start looking at ECU's to address the gearchange problem. As far as the shimmy goes, are you tyres at the correct pressure - and all the same (or at least the two front and two back being the same)?