Rathuris said:
Is it possible for half-breed monster to be male?
How much does a half-breed character take after their monster heritage?
Yes, and most half-breeds are male. Females always match their mother completely, though one extremely unique event can occur where a mamono births a female human child. Females can never be half-breeds.
How much a male takes after his mother in appearance can differ, though the limit is 50/50. They must still be recognizable as a human despite any changes that occur, and they always maintain the same basic physical body of a human being. Two legs, two hands, etc. They may also develop small traits from their mother. Males may grow lesser wings that allow them to glide, but no male of an avian beast may ever compete with a female avian and win in a race. No male of a minotaurus(female minotaur) may ever win in an arm wrestling contest with a female of the same race. So while they do adapt somewhat from their mother's strengths, the adaptations aren't very strong.
Rathuris said:
Does this mean half-breeds tend to be feminine in appearance?
So monsters such as any demon, slimes, dark matter, or undead do not create half-breeds?
No powerful natural powers such as fire breath, right off the bat correct?
Also if the mother's diet is a man's fluid does that carry over to the child?
Basically, very few things actually carry over besides some basic appearances. It's safe to assume a human male with some monstrous appearances is about as threatening as a normal squishy human.
Men can still look like men. Their appearances can vary greatly, as per normal difference in human features you see day by day.
Men also cannot be born from mamono who reasonably cannot birth anything but themselves, thusly including slimes and the like, though demons can still birth males. Undead also usually cannot birth anything at all, unless their sexual organs have been preserved. (Dullahan are the most common case, where they're considered undead because their head was severed from their shoulders, but magic maintained their body and prevented it from dying.)
Also, men never crave another man's semen for sustenance.

If they ever do, then it's their sexual preference, and does not aid in their survival.
Rathuris said:
I take it no special powers for half-breeds like the wyvern's or dragon's full transformation power or the doppleganger's shapeshifting and mindreading?
Wyverns and dragons can only transform because their immense power allow them to do so. Male children are obviously denied this ability by default because they will always possess a lesser soul.
But some abilities can manifest. In the case above, the doppleganger, a male 'might' be able to perform various degrees of mind reading by default at birth if they possess greater than average power within their souls (this is an uncommon case). But something like shapeshifting occurs because the doppleganger has no actual shell (aka, a body) and and reshape their threads of magic at will to take any form they desire. Males will always have a normal body. That is, one that is of a fairly consistent shape. Any changes that occur to their form is either an illusion cast by magic, or permanent alterations (the dangerous kind).
Again, it's still safe to regard a half-breed male the same as a normal human. Any traits they get from their mothers are outshined by potential they can achieve through other means, such as learning the ways of weaving (magic), or developing physical skills.