There are a couple of ways to go about those notches without having to do hand work like chiseling.
They are effectively the same except for the orientation of the seat panel itself. So the choice comes down to the tools you have available really.
First is a table saw sled with a vertical support for clamping the part in place. Set the panel to one angle, the blade tilt to the other, cut one side of each notch, then reverse it all for the other side.
This could be done exactly the same way with a track saw, just cutting from above instead of the blade being below.
The Domino part is the conundrum. You cannot cut the mortices into both sides of a piece, with a notch, like that.
It won't go together like it would with loose aprons.
Strength is a relative issue. If this a small display table, plant stand, etc. it might be fine like this.
The bigger the top gets, the more need you will have to support the legs better. A lower apron will help a little, but tying them together with a lower stretcher would be the best. This would be especially important if it would be used as a stool.