@MRC01 provided a detailed reply to most of your questions. In practice, as far as headphones/IEMs are concerned, the main benefit of balanced amp (desktop or DAP) outputs is that they can provide up to four times more power than their SE outputs, if the amp uses a fully balanced differential circuit topology. Not relevant to you with a desktop amp, because your Sundaras are easy to drive (lower impedance, higher efficiency), and would not need that much power. However, with the BTR5 the difference between 3.5mm and 2.5mm outputs (more power from the latter) may quite possibly make a difference as to whether your Sundaras will be loud enough for your enjoyment. The other benefit of switching the current 3.5mm plug cable to a 2.5mm or 4.4mm plug balanced cable is the similar to MRC01's comment about the 4-pin XLR plug: you can then connect the Sundaras to any headphone output be it balanced or unbalanced with an adapter if needed.
What MRC01 is saying is that if you have a headphone cable terminated with 4-pin XLR plug, you can simply plug it into the balanced output of any headphone amp that provides one (these are almost always XLR jacks, a few desktop amps like the Topping A90 are starting to offer 4.4mm in addition). And use an adapter to connect the headphone to any SE output of any amp. If instead, the headphone has the usual SE plug cable that almost all of them come with, then you cannot use an adapter to plug it into a balanced output of an amp - you would need to replace the cable as you plan to do.
When it comes to interconnect cables between DAC and amp, adding to what MRC01 said, the principal benefit of balanced interconnects as I see it is that they help avoid issues of ground loop hums and other buzzes and noises that you may (or may not) encounter with single-ended RCA interconnects. If the RCA SE interconnects do not suffer from any noise problems due to improper earthing/grounding of the DAC and amp, the sound quality difference between RCA interconnects and XLR interconnects will be inaudible.
The connectors are expensive partially because there is quite a bit of manual labor that goes into making them, including the Litz weaving and the soldering and testing. These are not mass produced using machines. Also, the XLR and 4.4mm plugs/jacks cost a bit more than the very common 3.5mm SE versions. Also, I think the fact that these are niche products, desired mainly by audiophiles willing to pay a bit more, factors into the price too. You get the silver-plated oxygen-free copper slant to them, whether it makes any audible difference or not.