I’m not female (obviously), but from what I understand menopause it’s your body shutting down the ovulation cycle. This means a change in hormones as your body transitions from being ready to have babies to not being able to do so anymore.

It doesn’t mean you don’t have hormones anymore or lose your sex drive, but from the research I’ve read, the onset of menopause and years beyond middle-age means a decline in sex drive. Certainly this must vary from individual to individual.

So, to answer your questions:
1) Yes I believe you will though the frequency might decrease.
2) I would imagine you would still. This natural lubricant doesn’t occur from ovulation but to aid in intercourse. Worst case scenario, buy some lubricant.

As far as men, I know that our drive decreases with age but very few ever stop getting horny or getting erections. I know that sperm production decreases dramatically after child-producing years but I’ve never read about a complete stop to ejaculation.