Project desktop vs Planner + project Plan 3

There is no connection between MS Project Desktop and Planner.  Project online and Project for the Web have both been sun-setted (end date for Project Online is 30 Sept 26).

The guidance provided by MS for Planner is split over the old Teams planner, MS Project, Project Online and a CRM Dynamics solution. It is very confusing.

In terms of managing multiple projects you can either buy a solution from a third party or download and install the Microsoft project accelerator, which is a Power Apps app created by Microsoft. it is an old solution and is still branded as 'Project'. It also comes with a bespoke Power BI report. The PowerApps app allows you to organise plans by programs and has  out of the box fields for cost, state, stage, RAID, etc.  There are licensing implications so you might need to upgrade to Plan 5 to use all of the features you need.

Custom fields: I have tried to solve a similar problem by creating template plans with the custom fields, and copying the template plan in planner.  Custom fields are clearly somewhere in Dataverse, but there isn't currently an API to surface them. The only way I found to report on custom fields was to download the plans as excel files and aggregate the information using Power BI.

In terms of the dates if you are pulling data into Power BI then you can use Power BI date tables and connect to the task start and finish dates to organise by quarter, year etc. It is possible to pull out data on a daily basis relating to schedules for uncompleted tasks, (try the Resource TimePhase table) but not for completed tasks.