For badges here are a couple links you may find helpful.
Global Badges: https://badges.twitch.tv/v1/badges/global/display
Channel Badges: https://badges.twitch.tv/v1/badges/channels/CHANNEL_ID/display
For emotes, the Get All Emotes endpoint is one option (although as the docs warned, this does contain a lot of data). Depending on your use case, if for example you’re getting an emote ID from chat and just want the URL to display it then you can use
http://static-cdn.jtvnw.net/emoticons/v1/EMOTE_ID/SIZE or for bits the Get Cheermotes endpoint can be used to get the various different types.
There are also 3rd party sites such as https://twitchemotes.com/apidocs which some of us devs use too.
The docs are pretty bad when it comes to emotes/badges as the official API endpoints in this area are themselves bad/non-existent, so undocumented endpoints such as some of those I’ve linked above are often all we have, and the info that we do have in the docs is in various places, with some of it being in the V5 or Helix sections, other parts are in the Chat Section so if you haven’t already read through the chat docs I suggest you give that a read as that may help.