Where should I put my custom applications? I have downloaded some third party software, should I just put under /Applications or should I put under my home folder, e.g. ~/MyApps/?
It depends on what applications you want to keep to yourself and which ones you want to make accessible to all users:


Applications stored in /Applications are installed for all users.
The ~ stands for your home folder.
Applications stored in ~username/Applications are only for access by the user username.