So I'm not sure if this will work since you mentioned you don't want it linked to an email account. But the default google calendar is quite good, you can share schedule IE Sarah and I have a calendar for each of us shared with color coding so I can keep track on her appointments in town etc. That way we can plan things a little easier. It also does all the recurring schedule stuff you're looking for along with changing the time it alerts you. Another perk is you can log into it on the website version and make changes etc and it's persistent across any devices tied to that account.
Really I think that's the biggest advantage to the google setup, is the persistence across devices. My tablets, laptop, computers, phone etc all have the same information all the time.
Must have apps for me:
Tapatalk(it's a PITA compared to what it used to be, but better than other options IMHO)
Facebook for pages(to respond to customer stuff on Facebook, only needed if you run a business type of facebook page)
Messanger(also facebook but I do allot of talking via this with customers etc)
OGYoutube(Youtube replacement that allows all sorts of stuff like leaving the audio running with the screen off etc)
Wellsfargo app(manage my bank account and transfer funds, deposit checks etc)
Package Buddy(tracking incoming packages)
Drudge report(news etc)
Weather channel app(Prefer this, allows me to pull forecast as well as radar)
Yatse Remote(Remote control for my tv box using Kodi)
Unified Remote(PC computer remote control, works well for all sorts of stuff)
And there are probably more;) But those are the ones I use pretty much daily, and all I've had pretty good luck with. You'd have to sub your own for a few but that's the roles so to speak I use it in.