As far as the gadgets go, I'm not entirely sure. I accidentally bought a fire trail. Which when activated has this firefly thing buzzing around my head. So I'm assuming they're all on the same par as that.
As far as homes go, it refers to how many Teleport locations you can have. You automatically get one. Which you can set by doing /sethome then. Once you need to return to home, you type /home.
The dirt shop allows you to set 5 TP positions. In my opinion the diamond home is well worth saving for. If you do the quests in game you can easily build up your DCD account.
To then set a second home you stand in the location, and type "/sethome <name> "
To return there you type. "/home <name>"
Alternatively you can do /menu. Then click the door icon and it will give you a list of all your home locations.
Hope that helps. But be certain to check out the FAQs page on dogcraft.net/FAQs.php
It has lots of useful commands.
Happy exploring.