Joint and Groups clarification

If you joint objects

1 ) select several objects
then CTRL J
this is creating a new object from 2 existing objects
and there is the restriction of a maximum of 16 colors for one object
Meaning that if your joining a lot of objects you may loose some colors!

2 ) Group witht the CTRL G
Can we loose colors with these scheme:confused:
When we copy Alt D SHIFT D it copies all object in the group:confused:
If we append to another file does it copy all objects in the group:confused:

When and why should you use the group or joint option:confused:

Tanks & Salutations