How does "sharing" of purchased apps work on iPhone and iPad? If I buy an app for iPad or iPhone, then login to my account on a few other iPhones and download that app, are there any restrictions on how many devices I can install that application on?

Once I've downloaded the app to the maximum amount of devices, will my restriction be lifted if I delete the app on those devices?

Basically, how exactly does installing apps, with the same account, on multiple devices work?
There isn't a limit to this (or there isn't yet a limit that is imposed by Apple); you should be able to install iOS apps that you purchase on all your iOS devices (obviously using the same Apple ID).
From the Apple iTunes Terms of Service:

APP STORE PRODUCT USAGE RULES
(i) If you are an individual acting in your personal capacity, you may download and sync an App Store Product for personal, noncommercial use on any iOS Device you own or control.