How well do the reminders work on the Apple Watch? Would I be able to set a reminder Monday-Friday to continuously go off three times a day throughout the year?
The notifications can be set to mirror what you have on your iPhone - so, yes, if you setup the reminders as you've outlined they will also show up on the Apple Watch - the only caveat is if your paired iPhone is unlocked, the reminder will have notified you there so it won't also notify you on the watch.
I'm relatively new to the Apple Watch - having it for about a week now - I wasn't sure what to expect but one pleasant surprise is that notifications (reminders, texts, phone calls, etc.) that I receive on the phone but don't notice - I do notice due to the haptic feedback.
I was also traveling and using Siri/Maps to get to a destination - i kept getting pinged on my wrist before I had to make a turn - it is a very welcome feature.