Yes, it is possible to install on a mobile home. Please use suitable screws and plugs to it to your mobile home, consult with a local expert / constructor. Please make sure there is enough space above the door in order to install and easily open the door.
Yes, it can be mounted on a wood house. Please consult with an expert / constructor with regards to the type of screws and plugs you need for your specific wall type. (Screws and plugs for wood are not supplied).
It has to be sealed to the surface it is mounted onto, in order to prevent water seepage. It can be mounted onto a compatible (self-made) board that will provide a unified, solid space to mount the product onto. Make sure you secure it with suitable screws and plugs.
Yes, it is possible to install on vinyl sidings, make sure you used suitable screws and plugs for your wall type. A kit suitable for mounting on vinyl siding can be found online.