> my calendar (org-gcal)
Can org-gcal show calendar notifications? Can it access shared calendars?
> my email (mu4e)
Can you see and/or compose HTML mails?
> my pdf reader
Can you open and render correctly complex PDFs? Graphs, tables, images, tables of contents, maybe even forms, etc.?
You could probably get notifications using org-alert.
Emacs does a reasonable job parsing most html including emails to text, but occasionally you may need to view in browser if it's very html heavy. You can compose html emails using org mode syntax with org-mime.
PDFs are rendered as images. So you have limited emacs functionality, but it does a good job rendering PDFs. Doubt you can do forms.
No support for retina screens on Macs though, unfortunately.
I wrote an Emacs package that allowed me to render my emails in that way Outlook does it (comments on top, everything HTML). I write my emails using markup, and then it's all rendered prior to sending.
I had people mention how pretty my emails were.
HTML emails also render fine, with all images as you would expect. Emacs does support online images.