If you mean Homey (cloud), the app:
Here you’ll find all Homey cloud compatible brands and models:
You can use the search bar, but make sure the “homey switch” is set to “Homey” on the left.
TP link is supported, but you’ll have to check which models are supported.
Tuya wifi is not supported. The bridge can’t connect to local network devices.
The wifi part is exclusively used to connect it with internet via your wifi setup.
Tuya zigbee is partly supported, while you can use the Homey Zigbee ‘app’, to control devices basic on/off (relay, switch, smart plug) and for lights dim and color can be controlled in addition.
Keep in mind not all zigbee brands / models work well together;
Like, Aqara sensors work well with Homey, but not combined with Ikea tradfri lights (when they are in range and therefore can use the Tradfri router as hop).
Yes, but the bridge has nothing to do with free / fee. It’s just a piece of hardware which adds local radio protocols to Homey (and Wifi is NOT one of them, to be clear).
As you can see @ screenshot from the app, the marketing folks are very stubborn / misinformed / hope to sell more using little lies, and still advertise with wifi being one of the protocols 
You can use Homey for free with max. 5 devices, no time limit, the bridge is not regarded as device as such.
So it’s more like a very basic demo Homey without a subscription.
Also it lacks Logics, Variables, Insights, Advanced Flow. It will be unlocked when you buy a monthly €2.99 subscription, but, you can try it for free for the first month.
This info is present in the app:
Afaik there’s no possibility whatsoever to program things in the Homey app.
When you want to write an app yourself, Homey cloud is not really the place.
To publish an app you need to be a company, and pay a €100,- yearly fee.
In that case you’d better buy a Homey Pro, which even has a community app store, and you can install apps from Git f.i. by using the command line.
