Fan is loud and kicks on every couple minutes when idling

These sounds normal but it may help to get a recording if possible of the clicking. Any time I hear someone call it a click at idle, I go to injectors. These will actually make a clicking noise when they are firing. The other possible item are lifters but this is more of a tapping or rapping noise that can get worse when RPM goes up.

As for the fan kicking on, that is normal. It is a plastic fan (see below) and it will be loud at times because it kicks into high to keep the motor cool.

As for it taking a little while to warm up, this would not be a concern as long as it does reach operating temp and stay there. It could be a stuck open thermostat but we would need a little more to go on for that. Can you time how long it takes to reach operating temp? Meaning the temp gauge needs to be at least a quarter of the way. Also note the outside temp when doing this and we can get an idea if this is too long.