Question no.1: No.
It doesn't work that way, that's like saying you catch a level 60 graveler for example, if you max out the EVs will it get a +50 stat boost upon the next level up in Defense, no it won't.
Question no.2: Yes.
If you put a Pokemon in the DayCare with no EVs it won't get any but if you max them out before putting them in, it will level up as usual getting those stat boosts.
Hope I helped!