In the Lord of the Rings movies, Wormtongue is depicted as having black hair, which is out of place, since the Rohirrim all have blond hair. Is there any in-universe reason for giving him black hair?
Since Tolkien himself never wrote anything explicit about Wormtongue's hair colour, that must be considered a Jackson-ism. However, it is interesting to ask if it's possible for one of the Rohirrim to have dark hair. Let's look at the evidence.
We know that the Rohirrim were distant relatives of the old House of Hador from the First Age, being descended from those of that people who never made it over the Blue Mountains into Beleriand.
The Northmen appear to have been most nearly akin to the third and greatest of the peoples of the Elf-friends, ruled by the House of Hador. [Author's note.]
(Source: Unfinished Tales, Cirion and Eorl.)
What can we find out about the House of Hador? In HoME 12, "Of Dwarves and Men", we see the following description:
For the most part they were tall people, with flaxen or golden hair and blue-grey eyes, but there were not a few among them that had dark hair
Furthermore, in LotR Appendix A we actually meet one of the Rohirrim who is explicitly mentioned as having dark hair:
There was at that time a man named Freca, who claimed descent from King Freawine, though he had, men said, much Dunlendish blood, and was dark-haired.
I've italicised "men said" here as it has bearing on the next point: be very careful about extrapolating from what Tolkien wrote, especially if what he wrote was written in character. What you read is not an objective description of the way things are, but rather an in-character interpretation. Therefore Tolkien did not write that Freca had Dunlendish blood; what he wrote was that men said he had Dunlendish blood - in the latter case the possibility that his Dunlendish blood is just nothing more than gossip, rumour, filth and lies remains open. This may seem verging on the pedantic, but given Tolkien's credentials it's important to get points like this right.
That brings me to that next and last point:
Death to the Forgoil! Death to the Strawheads! Death to the robbers of the North!
Again, it must be emphasised, do not extrapolate. These are words of the Dunlendings, intended to be insulting (a racial slur, even); I mentioned in the comments that it should be viewed in the same light as the word "paleface", which we're familiar with from matinee westerns and which is not an accurate description of all Europeans.
Just to reinforce the point:
The men of Dunland were amazed, for Saruman had told them that the men of Rohan were cruel and burned their captives alive.
Again, this is an in-character description of the Rohirrim, but this time it's explicit; it doesn't always need to be so, however; if it's in-character you should always treat it as being potentially influenced by that character's opinions and prejudices.
So, even though Wormtongue having dark hair is entirely a Jackson-ism, it's perfectly explicable and consistent with what Tolkien wrote.
None that is specifically mentioned in the novels. We know nothing of Grima's childhood save that he was the son of Galmod.
However it may be a subtle reference to the Dunlendings, who were foes of the Rohirrim having been displaced by them. That is just speculation though.