this site recommends i eat 1,200 calories a day?!?

Because you chose 2 lbs a week. It is simply a calculator. It relies on you to choose appropriate information/goals. That is a 1000 calorie deficit (it is likely that puts you under 1200 but that is the lowest the site will go)
You also likely chose sedentary, which few people truly are.

Also, this site expects you to log exercise and eat those calories back. So if you do any exercise, you would be eating more than 1200.

With 20lbs to lose, .5 lb per week would be a better option. No more than 1 lb.

That's before adding in your exercising calories. As you log your exercise, it will give you more calories to work with every day. And pretty much any activity counts as exercise, as even house cleaning is available in the database.

I'm at 1200, but it is really difficult if I don't workout. If I do workout, it's very easy. And I have lost weight at a really great pace. Not too fast, not too slow. And I'm not hungry. However, I still give myself 1200-1400 calories a day. I don't stick to 1200 firmly. For me seeing a red 160 for my calories is no big deal. For me, it's been about changing the types of foods I eat and really helping to keep me on track for working out. So it's worked for me, but a lot of people just up their calories and still lose weight very successfully.

Don't cut 2lbs a week then. That's 1000 cals a day less that you would have to eat.

Go for 1lb a week and hey presto you can eat 1700 a day, is that a healthy enough amount for you?

Not necessarily. That would only be the case if MFP figured her maintenance calories at 2200 calories. It is possible that it might be under there, however, MFP won't go lower that 1200.
For example, my maintenance at lightly active is around 1900. If I choose 2 lbs a week I get 1200. If I change to 1 lb a week I get 1400.

If you set it to "sedentary", that 1200 basically assumes you lie on the couch in your undies all day. You get to eat back all your exercise calories too.

how much walking would bump this up to the next level because i do VERY little during the week other than walking my dog a mile a day.

Keep in mind that the activity levels on here have no exercise included, just daily living so that mile walk would be logged.

Check out the Activity Level Setting. It tells you what sedentary and lightly active are, so you can pick the one closest to your truth. If I'm remembering correctly, lightly active has an example of a sales clerk or teacher on her feet for a majority of the work day. That's why I chose sedentary. But logging my water aerobics and mall walking gives me more calories to use each day, so sedentary isn't such a bad setting for me.