As far as DMXIS goes, please see this post (I would recommend getting an Art-Net node instead):
Regarding Ableton Live performance issues, it unfortunately sounds like you were close to the limit of what your computer can deal with and with Beam devices added to your Live Set that threshold is crossed. The Intel series of MBPs from that era suffer from overheating, which results in throttling (CPU slowing down to decrease the temperature) and spikes in performance. While many of those machines have quite capable hardware on paper, these issues make them unreliable for live performing.
The Mac computers with Apple silicon (even a base model Mac Mini M1) offer a much more stable and predictable performance.
Please let us know how it goes with your M1 machine in this regard.
It is a bit unfortunate that my answers to both of your issues are basically “buy new stuff”, but as a small software team we can only offer so much support for hardware that was not designed to last.