1-I'm not using instagram's API, those limitations do not apply to Statimgram.
2-Idem before. We save (encrypted) username and password. We don't send "reminders" like hootsuite or other solutions, we post directly into IG.
Here's a small (this is 5 months old, the new UI looks much better!) demo: https://www.youtube.com/watch?v=mGwV6lBi8Us
Using this to sort out your own problem would probably fine as they will not notice it, but selling this as paid service might cause some trouble for you with Instagram Legal and also at the same time if you keep using same IP Instagram will probably block your APi after some time when they sense the usage.
Just a friendly notice for the things you might face in near feature :)
Edit: because reverse engineering their api is also against their guidelines. Just because you don't use their official api, doesn't mean you don't have to adhere to their rules.