1) Yes. You can create new objects related to existing ones. We have done it for Applications, with now 4 levels.
2) Sure, you can delete any object in the model, as long as you don't break the allocation logic. @Renee Daignault's answer says it well.
3) We typically keep online 2 years. We found that closing periods is not very useful, as it only prevents us from loading new data to the closed periods.
- In the Time Settings we move forward the project start date (currently DEC2020):

Before I push the date forward, I extract key data based on a report, so that we keep past history.
- In the Calculation Settings, we limit the pre-calculated months:

#ApptioforAll