Does the Roku Express 4K+ model have functions to search for free over the air channels and live TV?
None of the Roku streaming devices will allow you to natively receive free live antenna/over-the-air channels (OTA). The devices themselves do not have a TV tuner and present rules do not generally allow streaming services to provide these channels for free. (due to broadcast and transmission fees/licenses).
The only way to receive free OTA is to connect an antenna to your TV or your Roku TV. A RokuTV is a manufactured television that has an integrated Roku operating system. This is different than having a television with an HDMI connected Roku device like an Express or Express 4k+.
There were some streaming services (Locast) that attempted to provide free OTA channels pretty recently (maybe a year or so), but the broadcasters came after them and shut them down with a court ruling. Until someone figures a way that meets legal requirements, an antenna is going to be the only way to access these OTA channels for free.
There are some cable-alternative streaming services like Hulu w/LiveTV and YoutubeTV that offer packages with local OTA channels but these will be paid subscriptions ($65+/mo).
It should also be noted that the 3710 and 3910 (both shown below the initial post) are not even 4K models; they only support output resolutions ranging from 480i (via Composite) to 1080p (via HDMI). I own the latter model.
Plus, with ATSC 3.0 coming up in the next few years, I do not know if the digital OTA converter boxes (which are meant for obsolete analog sets) will continue to work or not. Some of the OTA converter boxes made today are generic no-name brands, and support up to 1080p but I have no idea if the newer OTA boxes will work with ATSC 3.0 or not.
~ Jordan