A dirty under-carriage is actually quite harmful. It harms the metal body wax. There is no harm in going to the sevice station for a wash under the car. They will lift the car and wash with plain water. No Aayl.
Another way which i learnt by @vague_one was to take two hydraulic jacks and lift up the car. Take a skate board and go under the car with some apc or presoak and rub the dirt loose. Hose off!
He first option seems more practical, lets seewhat ahmad bhai says! 
And for the chrome exhaust muffler-you can use ice liquid clay like ehsan bhai has done a few posts ago...
However i think you should try Turtle wax chrome and metal polish. It gives very professional results in less effort. I'll post results of this product in a while.
