I don't think there's anything that would have all included. Problem is that FB for example took down their API support few years ago, forcing more traffic directly to their site.
You have quite a lot to follow. Are all of those really that important that you need to watch them constantly? Or could you change your habits to check some twice a day for example.
I don't have all-in-one solution. But I can give you few options. For example Opera browser has sidebar tools, giving quick access to some IMs and other such. Including Messenger, WhatsApp, Telegram, Twitter etc. You could use tabbed browsing for online feeds, such as FB and LinkedIn, also calendar if it has web UI.
I use web version of Google Calendar on desktop, and aCalendar on mobile. This does require some manual work to get school and work stuff in there as I can't sync them directly. For email I use BlueMail on mobile and Thunderbird for desktop. For me using more software is preferred as it means I can configure them exactly how I like.