Electrical – RS485 half duplex mode in full duplex IC

Coincidentally, I just completed a project using the same rs485. Add a pull-up resistor at DE, and a pull-down resistor at 'RE. This way, you will always be ready to either receive or transmit. (10k pull-up, 220 ohms pull-down) Do this for both ICs. Do not leave either of these pins floating. Good Luck!

No. A converter merely changes the electrical signalling and gives you an explicit (typically modem control line reuse) or automatic (time based) control of the transmit enable.

Adaptation to a half-duplex scheme must be made by the software at each end.

As for why exactly your setup failed, that is impossible to answer with the limited information given, however it software not written with this mode of communication in mind could be a key part of the problem.