Hi everyone.

I have an European HK MR223 A3 rifle. Can I change my factory buffer tube out with Battle Arms Development buffer tube?

And what happens if I put a mil-spec carbine tube on rifle that runs an A5 tube and vice versa? I don't even know what type the HK buffer tube falls into?? Any idea anyone?

While the Mil-Spec & Vltor A5 tubes are the same diameter, they are not interchangeable in and of themselves.
The A5 uses a rifle length spring and a proprietary length buffer.
Put a carbine spring inside and it would lead to it being under sprung and probably throw off the timing.

The other way around, you'd have a softer rifle length spring crammed into a carbine buffer tube. I would imagine it would lead to FTEs galore.

The HK Buffer tube is just a standard tube with a proprietary spring and buffer (same size as mil spec, just proprietary coils and weights). The HK spring is longer than normal, and the buffer slightly heavier than a H2... Changing any of those to Brand X of the same weight or setup honestly will probably hurt you more than anything as the HKs are overgassed pretty bad from the factory. If you switched to the Vltor A5 setup ( I did on my last MR556), it will shoot softer and I recommend the A3 buffer with it as it is heavier than the HK and will slow everything down.

As stated above, you CANNOT mix and match A5 and standard carbine components.