Is mid February a good time of year to visit? How long do you need to enjoy the area and can it be a good day trip from eastern Los angeles?

Yes but you need to get there till 5. You can enjoy the park for like an hour or two

I would visit in February but you might get snow. You can see the highlights in a day but I would recommend a long weekend so that you can get some hiking in. Don't forget to check out Joshua Tree tavern for some local flavor. JT is a magical place.