It works like this:
The DNG profile contains "color matrices", these are not used for actual color rendition (the forward matrices are used for that) but as a way to estimate what a specific combination of raw red + blue + green means in terms of light temperature and tint. When you make a new profile, using X-Rite's software, my software or anyone elses, they will calculate their own color matrices. The problem is that having just three raw channels (RGB) is totally inadequate when it comes to calculating a light temperature, and on top of that there's no standardized definition of light temperature + tint. This means that different software will make different color matrices, even if shot under the exact same conditions, and it will result in different temperature+tint combinations. In the daylight range (5000K - 6500K) it's not uncommon that two profiles can differ up to 500K in their estimates.
This would not have been a problem if Lightroom just presented temp/tint as a "fun fact" and handles for sliders. However, as soon as you change to a custom white balance Lightroom will store the temp and tint as your white balance setting. It does not care about the actual RGB multipliers that is applied on the raw data. When you load a file it will thus check temp+tint, run that through the profiles color matrices to get the RGB multipliers and those are then applied.
That is if you change profile to one with different color matrices than the previous profile, the resulting RGB multipliers will be different and thus you get a new white balance.
"As shot" is an exception. In this case Lightroom will take the RGB multipliers directly so the tint won't change when you change profile, but instead the temp/tint combination change as it then calculates it the other way around: it takes the RGB multipliers and feed it to the profile color matrices to get a temp tint estimation.
Temp/tint is a very bad unit for white balance if you want something well-defined and stable. But it's something that is more intuitive than three RGB numbers to us photographers. The least bad solution would be to always store RGB multpliers but show temp/tint in the GUI and let the temp/tint jump around a bit when you change profile, that is always run it like in the As Shot mode. But that's not how they do it.
So to the questions;
1) no it won't make a difference if you export a DNG and make the profile elsewhere. The only way to not have this effect is to copy the color matrices from the original profile.
2) On the raw level white balance is always RGB multipliers (unless you have some exotic camera with other channels than RGB), but as a user you never get to see those directly. Different manufacturers have different ways to translate those into more user-friendly numbers, usually a temperature+tint combination. However as said there is no standard how this is done, and even if it was the three RGB channels are too few to make an accurate conversion. That is your camera's understanding of what 5300K is is probably a quite bit away from what Lightroom's standard profile 5300K is. But anway, say you set a custom white balance in your camera that makes your patch perfectly neutral this means that you can leave the WB in Lightroom at "As Shot", and then you can switch profiles without getting a shift. So yes in that case it makes a difference.
What kind of Canon 5D do you have? 5D mk III, 5Ds? 5DII, original 5D?