The undercarriage isn't designed to take large lateral loads, however I would have thought that sharp cornering was more likely to take the tyres (tires) off the rims rather than damage the landing gear.
"Greaser" landings aren't ideal in commercial operations. A positive touchdown is preferred especially when surface contamination is present (water, slush, snow) as this punches the rubber through to the runway surface giving positive contact and allows for better braking efficiency.
The runway exit to use is assigned by ATC, but may be of the form "Exit next convenient right". Safety is overriding here ... the pilot will not accept an exit that he/she can't sensibly make.