The contraceptive mandate covers all female contraceptive methods except for condoms.
Not true.
With some very minor exceptions what I said is true. Some tiny fraction of women might be slightly inconvenienced by the fact that Nuvaring isn't covered but that's nothing compared with the very large number of women who have to pay for their condoms.
Essure
(Essure says you might be covered by the ACA)[http://www.essure.com/getting-essure/health-insurance]
Nuvaring
That doesn't include a lot of different formulations
Yes, it seems like if a generic alternative is available, they do not have to provide you with the name brand pill at no cost.
and they cover vasectomies 100%.
No. No insurance covers vasectomies at no cost to the patient. It isn't a big deal but it's still surgery. The doctor probably bills your insurance a couple grand once everything is paid off. As the patient, at a minimum, you pay a co-pay twice.
I've never had an insurance policy that didn't cover them.
The same goes for tubal ligation (even Hobby Lobby's insurance covers Tubal Ligation). What the ACA did was was to reduce the cost of contraception completely. Meaning you and all other women can get a Tubal Ligation for free, whereas men have to pay something for a vasectomy.