Can I install a trail camera that will allow me to check it from the internet? Also from a smartphone that is within 100 feet of the camera?
Yes, as long as the camera is installed where you have a legal right to be, such as public land or permission from a private landowner.
Idah Code 36-1101 addresses devices accessed via the internet.
Devices Accessed via Internet.(A) No person shall shoot at or kill any bird or animal in Idaho, wild or domestic, including domestic cervidae governed under the provisions of chapter 37, title 25, Idaho Code, with any gun or other device accessed and controlled via an internet connection. Accessing, regulating access to, or regulating the control of a device capable of being operated in violation of this paragraph shall be prima facie evidence of an offense under this paragraph.