Hi Ritik,
Regarding access to ArcGIS Pro and analysis:
To download ArcGIS Pro, you can follow these instructions.
With your Learn ArcGIS account, you should be able to see the analysis options in ArcGIS Online. The fact that you do not suggests to me that you may have multiple accounts. Perhaps you also have a public account and are signed in with it instead. Please make sure you are signed in with your "_LearnArcGIS" username. If the site will not allow you to sign in with that username, so to https://www.arcgis.com/ and try there instead.
Regarding a learning plan for ArcGIS, I agree with Shane that it is important to know what your end goal is. The learning plan I would recommend to someone who wants to do scientific research is very different from someone who wants to apply GIS to manage resources for a municipality. The first person will never use some of the tools which are very important to the second person and vice versa.
Without knowing too much about your specific goals, I will recommend that you learn ArcGIS Pro using these resources:
Get Started with ArcGIS Pro | Learn ArcGIS (step-by-step lesson)
ArcGIS Pro Basics (web course)
Learn ArcGIS | Learn ArcGIS (path with a series of learning resources)