If your sick, does having sex really help make you feel better? And or help get rid of the sickness?
Not but having sex does release endorphins which, make you feel a lot better just based on chemical releases. It won't cure any illness though just make you feel more elated for a small while.
Not necessarily, but it depends on what the illness is.
It can help with headaches, because it relieves stress, but I don't recommend trying it when you have the flu.
Itchi is right. It depends on what you have. Generally when you have the flu it isn't good, because sex = exercise and exercise isn't good when you've got the flu.