Be careful not to use ' How's.... going' for everything, as it only works for THINGS that have a prgression or duration (e.g., a day, a project, a year, etc.) It cannot be used for people (usually you can use"doing" for people).
That is, in your sentences:
1) How's your wife going? WRONG Use "doing"
2)How's your son going? WRONG Use "doing"
3) How's your health going? WRONG Use "How's your health?"
4) How's your new term going? FINE!
5) How's the price of your house going? MAYBE but a bit strange, as a price is usually not something that has a progression or duration
6)How's your work going? FINE!
7) How's your trip going? FINE!
8)How's the relation with your boss going? FINE!!
9) How's your feeling going? WRONG. Use." How are you feeling?"
It's great to see you trying to apply something you've learned to new situations, but try to be ovservant of the characteristics of the original situation, to help you understand the "hidden rules" governing it use.
