The connector itself shouldn't be an issue, because it doesn't fall under IP. The shape of the connector is entirely functional, so there's no creative work involved, so it would fall under patent law. However, the connector itself is unlikely to be innovative enough to be patentable, so it's not protected by patent law either.

Using HDMI connectors is totally fine. You just can't label it as "has HDMI port", as "HDMI" is a trademark.

Is that true? There is obviously some creative work in connector design - optimizing for looks, robustness to damage, dirt, easy of use, reliability technically, etc.