Am I supposed to set TRIS as well?
The USART section in the datasheet for your device will tell you if you should set/clear the TRIS bits for the TX/RX pins.
If the chip supports open-drain mode then you just need to setup the TX pin to enable it at startup (ODCONC.6 = 1).
There's no need to set and clear it, and you won't need to enable/disable TXEN anymore either.

Add a pullup to the TX line (you say you already have one), and you can connect all the TX lines from the different pics together now.

If your pic has PPS you'll probably need to set that up too to assign the pin to the UART TXD function.
PPS output functions aren't typically enabled by default.