Yep, as far as I understand it there aren’t any exceptions to the limitations. Tweetbot, Twitterific, Echofon, they’re all subject to the same limits (technically existing client apps could have a higher user limit than 100,000 but that’s because they already existed when the limit was introduced, new apps are still limited to 100,000). I don’t know how other apps manage the rate limiting but Tweetbot uses the streaming APIs which as I said have different rate limits. Realistically though most of the rate limits are pretty reasonable for the majority of users; it’s unlikely many people are going to refresh their mentions timeline 15 times in 15 minutes very often.
The way access tokens work is part of the process of authenticating your account with Twitter to use the app, and is all documented on this site, but you should have that bit working already if you’re able to test your app; you are using API v1.1 which requires authentication for all requests, right? At a very basic level, when you go through the whole ‘Sign In with Twitter’ and OAuth authentication process, you go through and authorize the app to access your account, and you get back access tokens to make API requests on behalf of that user, which you must already have; if you’re using the Twitter libraries in iOS to do this then it should take care of it for you as far as I’m aware. For apps that replicate the core Twitter experience, only 100,000 accounts can go through this process, and once there’s more than that it won’t authorize the app, you won’t get any tokens, and the user won’t be able to use the app. As for taking it down, I don’t really know, that’d be up to you; I know Falcon Pro for Android had to hike the price up because it has to stay in the Google Play store to allow them to update it, but they didn’t want people to buy it anymore because they’d used up their allotment of tokens. Basically it’d be possible to buy an app that you can’t allow your Twitter account to use so you’ve wasted your money. This is why it’s discouraged to build apps that replicate the core Twitter experience.