Not sure “sequestered” is the right word here. I think “incorporated” would be better. Yes, the genetic material would have to be incorporated into a cell of the host genome. That’s what retroviruses do. It’s their modus operandi. If that host cell happens to be a germ line cell, there you go.
Again, modus operandi.This would have to happen randomly.
So the most likely time/place for a virus to infect a germ line cell would be when it is most exposed to the environment. I’m fairly certain the target would not be a sperm, mostly because 1. the sperm DNA is not in a form in which the retro viral DNA can be inserted (it’s super-compacted), and 2. the odds of any given sperm cell reproducing are minuscule (so sperm are almost always a dead end for the virus). So the most likely target would be the egg after it has been released into the Fallopian tube up until a short time after it has been inseminated and undergone several cell divisions. The germ line cell(s?) would still be exposed to the external milieux until the outside layer of the blastocyst is formed. And for what it’s worth, we know for sure that the “milieux” is full of material from an external source, because that’s what the sperm is, plus whatever viruses might be in the fluid.Maybe you have another mechanism in mind for the human genome acquiring viruses?
Let’s say for now the virus infects the zygote. The viral DNA would get inserted randomly into the host DNA, as you say. Actually, the insertion is probably not completely random. It is most likely to happen where DNA is somewhat exposed, i.e., where the DNA is actively being used by the cell. Now you mention that the insertion has to happen where it doesn’t disrupt the host code. This is true, but given, as mentioned in the video, that the human genome is about 90% “junk”, which just means non-coding for protein, there seems to be a lot of room for safe insertion. If the viral DNA destroys a vital function, that cell dies and is thus selected against.
So now if the viral DNA finds some innocuous spot, it just sits there and the host apparatus makes lots of copies of it, one for each cell.
Now if the viral DNA turns out to be somehow useful to the host, that host will be selected for survival, and the important viral DNA will be preserved, and possibly tweaked. The non-important (for the host) DNA will come along for the ride but will get mutated without effect on the host species.