Getting # of slots of an adjacent block and other inventory handling questions

Perhaps I'm missing something obvious but I can not for the life of me figure out how to dynamically iterate how many slots a block like a chest or dispenser has.  I'd like to be able to push items into an adjacent inventory which could be anything from a normal chest to some modded block with n slots.

In a similar vein.  putting an item into an adjacent inventory (like a chest) by having to define which slot which seems limiting.  I'd like to just put it into first available slot similar to how shift-clicking from your inventory into a chest does.  either add it to a pre-existing non-full stack or put it into an empty slot.  I'm almost sure I could maybe create a procedure to do this after a few headaches and tears, but I'd need to be able to iterate dynamically how many slots I'm dealing with.