Do older aircraft require increased general maintenance?
The very simple answer to your first question is just yes.

As something (or someone) age, more maintenance is required. It varies from case to case and you cannot have one size fits all rule or guideline.

FAA has published a thorough guide for maintaining older airplanes (PDF). For the relation of age on maintenance costs, this article (PDF) discusses it in detail.

Getting to your last question, it also depends on an individual case. Please also note that when an airplane is grounded, it is not required to be scrapped in all cases. Sometimes museums are interested in it, or it can be installed as a roadside monument or placed in an aircraft boneyard.

Regarding when an aircraft needs to be retired or scraped, these two articles are a good read:


When to replace an aircraft
How old is too old?