Abilities and features only alter the stats they mention. So if you'd need to drop your equipment it would say so. Think of it as holding your arms really close to the edge of the shell, not like a loony tunes style shell "plop" and you're fully covered by your shell. So to answer your questions:
Your equipment is still held, so no need to pick it up (again, if this were the case it would be mentioned like Wild Shape)
While in your shell you are prone, while out you are not (unless other effect caused you to be prone). I think if you were still prone after emerging it would say so, or the text would be "When you withdraw into your shell, you automatically fall prone". As is, you count as prone while in your shell, so when you're out, you're no longer prone.
About the shield, I refer to my previous statement; I don't think you go fully in (real turtles can't do that either) so yes, you'd still have your shield bonus, effectively giving you 23 AC (17 natural armor + 4 Shell Defense + 2 shield bonus), but you can't take any actions so I think that's a fair tradeoff.
When you go in in to shell defense:
What happens to say your Staff and shield? Do you drop them and then have to pick them back up?
When in shell defense and you emerge from shell as a bonus action, do you auto stand up (since it says "while" in shell defense you are prone)
or is it more of stance than a full withdrawal in to the shell? so you dont drop stuff then in that case?
If you do go in can you keep the shield to cover your shell opening and keep the +2 AC from the shield?
Abilities and features only alter the stats they mention. So if you'd need to drop your equipment it would say so. Think of it as holding your arms really close to the edge of the shell, not like a loony tunes style shell "plop" and you're fully covered by your shell. So to answer your questions:
Your equipment is still held, so no need to pick it up (again, if this were the case it would be mentioned like Wild Shape)
While in your shell you are prone, while out you are not (unless other effect caused you to be prone). I think if you were still prone after emerging it would say so, or the text would be "When you withdraw into your shell, you automatically fall prone". As is, you count as prone while in your shell, so when you're out, you're no longer prone.
About the shield, I refer to my previous statement; I don't think you go fully in (real turtles can't do that either) so yes, you'd still have your shield bonus, effectively giving you 23 AC (17 natural armor + 4 Shell Defense + 2 shield bonus), but you can't take any actions so I think that's a fair tradeoff.
Subclass: Dwarven Defender - Dragonborn Paragon
Feats: Artificer Apprentice
Monsters: Sheep - Spellbreaker Warforged Titan
Magic Items: Whipier - Ring of Secret Storage - Collar of the Guardian
Monster template: Skeletal Creature