Heat Pump Leaking Water Inside & Coils Iced

I'm a complete novice in the Heating/AC world, so maybe this is very elementary...
Our Rheem Heat Pump has begun leaking water onto the basement floor. We turned it off and later turned it back on and let it run for a while. Looking in the enclosed area under the unit, I saw water dripping down. Opening the side, I could see water dripping off the coils, but didn't see what looked to be a drain pan under it.
We had some minimal work done on this last winter (replaced the drain pipe to create a better angle for the water to flow) and it's possible something funky happened -- like they forgot to put back the drain pan. Or it's possible that this thing doesn't have a conventional drain pan -- or I'm not seeing it.
Turned it off again. Later turned it on and let it run for a couple of hours. No water, but when I opened the side again, the coils are iced up.
Not sure how old this thing is. The house was built in the mid-70s although many appliances have been upgraded since then. We just moved in a year ago. This problem didn't exist last year.
Any guesses or any place to send me to look?
Thanks
-- Michael Redman
--
mailto: snipped-for-privacy@bluemarble.net
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