These are mainly caused by the item (in inventory) being a different entity that the combined chest.
1. Blueprints with modular chests cannot be built.
(this is particularly annoying with regards to green/red wire connected to chests, as it would otherwise be done for free.)
2. Blueprints with modular chests cannot be rotated
3. Modular chests cannot be upgraded, even manually. (i.e. iron chests cannot be upgraded to steel without emptying them and re-placing them.)

I don't think it's practical to fix these issues within the current design. May I suggest that chests use the same entity, and point to a common inventory? IDK how difficult it would be to make inserters/clicking/etc use an adjacent entity's inventory, but if possible it would be a much cleaner solution, as it would not require special case handling for difference sizes, only for placing next is merging/spliting etc.
4.