The waste from sink will directly drain from the bottle trap. Bottle trap is more hygienic as it doesn't allow any gases from drain into the kitchen/bathroom.

The one on the floor is to allow any water (either from overflow or from cleaning the floor) to be drained out.

the on the wall drain and floor one are close to each other. so both go into a single cabinet. how stable are bottle traps? should i plan for leaks on a longer run?

If the bottle trap is of good quality, you need not worry. It might just need maintenance based on regular wear and tear. Else nothing to worry. Nest to each other is ok. The floor drain is to drain out any excess water from kitchen floor.