it largely depends on what you actually mean by "movies and TV shows".
Over the air digital TV broadcasts? OTA analogue broadcasts? Satelite broadcasts? Locally stored files? Files on another machine on your LAN? Internet streaming services? DVDs? Blu ray discs? DRM free or not?
If you can get the video in to the zeroW it should handle playing it though some formats may benefit from having the codec licenses. VIdeo playback on a A+ pi is fine and that predates the zeroW though they both use broadly the same CPU and GPU.
The TV hat will get you OTA digital TV in most places but check the specs against those in use where you live.
For most other broadcast services you'll need a USB device to recieve the signal and pass it digitaly to the Pi.
For streaming services, that'll largely depend on whether they can be acessed by a web browser or whether they're restricted to a service specific client. Even with a web browser, it'll depend on what features the browser must support and which browser you're trying to use. If you need a service specific client, it's unlikely a linux version exists and where one does, it's unlikely that a suitable ARM Linux one is available.
Locally stored files may perform better on USB storage than when stored on the SD card but that's dependent on the performace of the USB storage device.
If your intent is to bypass copyright (e.g via downloads, VPN, unofficial streaming services, torrents, etc) please don't ask for tips on that. They won't be forth comming. At least not from me.
Arguing with strangers on the internet since 1993.