Is home computers security safe from employer while networking to employers computer?

Answer 1

Most often, NO.

Technologically speaking your employer often requires installation of software commonly referred to as a VPN client and these VPN packages are more than capable of performing remote functions on your computer in a surreptitious manner or clearly visible manner.

Also, when you are connected to their network, any security issues and vulnerabilities will become exposed to their network and depending on how their network is configured, any co-worker you may or may not know or a co-worker that may dislike you enough to invade your computer.

Legally, many employers require their employees to sign acceptable usage agreements which may strip away most of your rights and expectations of privacy as much as they can before violate your 4th amendment rights while providing no warranties as protecting your computer from their network. These acceptable usage agreements often supplement language in their internal corporate policy which will cover and state you have no expectation and rights to privacy when using their computer equipment. Since you are plugging your computer into their network, their acceptable usage agreements for remote access may state as long as your computer is on their network, it is for all intents and purposes THEIR computer while they provide no warranties of support or protection.