Can I play 4K content on a 4K TV from a 1080P source such as a laptop via HDMI cable or would it play in 1080P on the TV?

As far as I know HDMI does have some form of support for 4K, but don't expect eery piece of hardware to be run perfectly with such (if anything, the setup you describe will probably be bottlenecked at 1080p if it doesn't complain about resolution formats).