is there a monthly charge for the service on the watch

What happens is you pay an extra monthly fee on your existing phone contract, the watch uses your existing phone number to make calls.In the US it's about $10 per month and about £10 in the UK,that is for the cellular version of the watch, if you buy the GPS only version of the watch you can make calls and send texts as long as you have your phone with you,with the cellular version of the watch you can make calls and send texts without having your phone with you.So in reality your paying $10/£10 a month so that you can leave your phone at home.

No, there is not, only if you get an AppleCare+ plan but that's an annual fee, not monthly

I pay $3.99/mo to keep AppleCare active on my series 4 Watch. I was offered this option when my original AppleCare contract was about to expire.