Yes, and yes.

And having two sources of 5V logic trying to drive the same wire results in them driving each other.. and perhaps frying each other.

When they are both at 5V, no problem. When they are both at 0V, no problem, but when they are toggling bits (alternating 5V and 0V in some pattern), then there are many instances where one is 5V, the other is 0V, and so the 5V is driving current backwards into the 0V line. Fried chips! [EDIT: because they are drivers, they have very little resistance to current flow, which means when 5V gets connected to 0V in this way, near infinite current will flow (Ohm's Law), and something will suffer. Badly.]

TX lines are always "drivers", and RX lines here are always passive receivers. So in the case of the Arduino TX-out going to the WT32i RX-in, the Arduino will be toggling between approx 5V and 0V for its bits, exceeding the voltage limit on the WT32i RX pin. Thus the need for the voltage divider.

The other way around, from the WT32i TX-out to the Arduino RX-in, no problem. The most the WT32i will output might be around 3-3.3V, and the Arduino is built to tolerate up to 5V there without issue. The important thing here is that the "1" voltage has to meet the Arduino's minimum spec for a "1", and that is usually between 1.8V and 2.4V (minimum) for 5V logic. So no problem there either.

Cheers!