Hi @Malvia
There's lots to unpack here, but let me start with the learning resources - this collection is maintained by the Power Apps team and contains everything from beginner to expert level.
Microsoft Power Platform: Learning Resources | Microsoft Power Apps
If you prefer videos, I would suggest to look at the YouTube channels of Reza Dorrani, Shane Young, Daniel Christian
In terms of your query regarding the App, you asked if it was realistic... this is an unrealistic expectation IF they are expecting you to only use Outlook, as your problem will be "Where is the data". If they are happy to use either Dataverse or SharePoint or some other datasource to store the data, then I think it can be done yes.
The first problem, is that you said they can't integrate with SharePoint/Teams/etc, but you will need to have somewhere to store your data. Yes it is possible to integrate notifications via Microsoft Outlook, but you will still need somewhere to store data to meet the other requirements (reminders need to have something to check to know when to remind, checklist answers need to be stored somewhere, etc.)
If they are willing to pay for licensing then you could store it within Microsoft Dataverse which is its own database designed for use with the Power Platform, and if they are not willing to pay for license then you will likely end p using SharePoint as it falls under most basic Microsoft licensing(E3 or higher) so they will likely already have access to that.
Despite what I've said here above, I would advise you to start looking at the learning resources so that you are able to confidently say whether or not you will be able to do this with the time you have. You should factor in the time it might take you to learn the platform as well as to build it.
I would suggest starting with the Canvas Apps paths on Microsoft Learn as this covers the basics of what you will need.
List of suggested learning paths here in order:
Introduction to the Microsoft Power Platform
Create a Canvas App in Power Apps
Navigation in a canvas app in Power Apps
How to build the UI in a canvas app in Power Apps
Use and understand Controls in a canvas app in Power Apps
There is also the PL-900 certification learning path which covers a lot of the technologies you'll need to build this requirement - PL-900: Microsoft Power Platform Fundamentals - Training | Microsoft Learn
Anyway, I know this will likely be information overload at this point, but do try start on one of the first links/modules and that should help you understand the platform a little better 🙂
If you get stuck with anything, post questions on the forums here and most times it will get answered fairly quickly 🙂
Cheers,
Sancho