Hi and welcome to the forum
If the disc was written successfully, then everything is good
The only exception is if you are using a very low quality disc, because with these crappy media often a disc is unreadable even just after the burn.
You can check if a disc has a problem running a verification process at the end of the burn (after a couple of minutes, so the disc can cool up a bit).
For example, you can run the read test with CD-DVD speed.
The drive buffer is never constant all the time. Little variations are normal. Actually, also big variations can be tolerated (for example, in my Pioneer 116 the buffer often varies between 100% and 40%) without problems.
Even if the buffer should be emptied during the burn, there are automatic mechanisms that temporarily stop the writing process until the buffer is full again, so the disc can be burned successfully anyway.
BTW, Burrrn is a software not more updated by a long time. I suggest to use a more recent software like ImgBurn. With Imgburn you can also run a verification test that compares the original files in your HDD with the files on the just burned disc. This test is more reliable than the read test done with cd-speed