Welcome to the WOA and welcome to sailing Jay.
After reading your questions, I would highly suggest that you try to find some other sailors around your area and get a mentor or at least just go sailing with some folks. Skippers are always looking for crew and gaining experience is fun on someone else's boat. This will teach you a LOT and FAST.
To answer your questions.
Standing rigging is rigging that holds up the mast. It consists of the stays (wires that connect the mast to the boat), the turnbuckles, the tangs, pins, and chainplates, etc. This standing rigging is typically made of 1x19 stainless steel wire and an "acceptable" replacement schedule is generally agreed to be between 10 and 15 years in salt water environments depending on how hard it was pushed. (or when an inspection reveals damage/problems).
The running rigging is rigging that sets the sails. Halyards lift the sails while sheets pull the sails into trim. The running rigging should be replaced as it is chafed or worn. This will depend very greatly on the amount of use it gets and how much sun exposure it gets.
Congrats on your new-to-you boat!