YES, ALMOST CERTAINLY MALE
The first question is easiest to answer: Tolkien tells us that Galmod is Grima's father! But we need to look a little deeper to see how.
The Rohirrim generally reckon descent from the father. For example, when Gandalf addresses Theoden, he says:
Hail, Theoden, son of Thengel!
Now Theoden son of Thengel, will you hearken to me?
We know Thengel was king before Theoden because he is so listed in the kinglist of Rohan and his wife was Morwen of Lossarnach.
Dwarves apparently reckon from the father as well, as Gimli is also spoken of in this way, as Gimli speaks of himself:
Then Eomer son of Eomund, Third Marshall of Riddermark, let Gimli the Dwarf Gloin's son warn you against foolish words.
But descent can also be reckoned from the mother --- when the mother is a kinswoman of, for example, the king. In Appendix A we read about the House of Eorl. There are no queens regnant in Rohan; and we know that when Helm Hammerhand and his sons perished, the kingship went to his sister's son, Frealaf Hildeson. Hild is mentioned there:
Soon after, the winter broke. Then Frealaf, son of Hild, Helm's sister, came down out of Dunharrow, to which many had fled; and with a small company of desperate men he surprised Wulf in Meduseld and slew him, and regained Edoras.
Note that it is important to name not so much the mother, in this culture, but her relationship to a prominent male relative. In this case, the king. In the kinglist, he is referred to simply as Frealaf Hildeson.
So, when Gandalf addresses Grima, he says only:
The wise speak only of what they know, Grima son of Galmod. A witless worm have you become.
So, what does all this mean? Given the above textual evidence, I believe it is safe to assume that Galmod is Grima's father, for two reasons:
- the lack of any "supporting" relationship to a male relative is indicative that "son of" refers to the father, and
- whenever someone is referred to as the son of his mother, the mother's relationship to a known male is never far away.
There are also secondary sources that assert Galmod's maleness:
In Complete Guide to Middle Earth, (R. Foster) we read:
Galmod (fl. TA 30th cent.) Man of Rohan, the father of Grima.
In Tolkien Companion (I. Tyler) we read:
Galmod The father of Grima Wormtongue, counsellor to King Theoden of Rohan. In the tongue of Rohan, his name means "sour-natured", a tendency clearly passed on to his son.
He is not mentioned in the History of Middle Earth or in Tolkien's published letters.
The evidence for Gamlod being Grima's father is simply stronger than for the opposite argument.
At best, I think it might be a fringe theory that Galmod was actually a woman. I am certain, as Gandalf had just had a lengthy and courteous discourse with both Theoden & Grima upon entering the King's house, he would not, even in a fit of temper, neglect to address Grima as "son of Maglod, So-and-so's sister" if that were the case.
As for the conversation taking place in Rohirric, that's entirely possible. And while it's possible for endings and other bits of grammar to become lost in translation, I think the cultural sense is pretty clear, and is not lost in translation at all.
As for the argument that Gandalf was simply making a funny, I do believe the consummate philologist and etymologist would have made hay somewhere, if this were actually the case.