For context this is an old basement floor drain in a 1951 Built House. The drain cover looks weird, the only opening is the hole where the pipe went down into it, it seems like the rest of the grate is sealed off somehow, but im sure theres no chance of me getting the grate off. 

When I bought the house the long peice was connected and shoved down into the floor drain, and there is a hole drilled in the back of the 90° that the condensate drain was connected to, it was really dumb because it would leak out all over the floor whenever you ran water in the sink, and because the drain grate is only open in the middle where the pipe went through, the water that would spill out around it wouldn't be able to go down the drain, so I decided to just pull the piece out to open the drain up instead. I want to fix it but the grate looks like somebody cemented it in so I don't think there's any chance of me being able to get it off to install a new one, so Im not sure what the best course of action would be here.

Is this drain supposed to have an air gap or is it allowed to be piped directly down into the drain? The small drain line is my condensate drain from my A/C and the big main one is an old slop sink. I removed the piece that went down into the drain to give it a proper air gap but im unsure on the be