harry potter - How do house elves breed?

The only information I could find on House Elf breeding came from the Wombat Grade 2 Test which was originally published on J K Rowlings' website website now resides on the HP-Lexicon.

In the Wombat Grade 2 Test we come across this question:

1. Which of the following statements on house-elves is FALSE?

a. House-elves have an average life-expectancy of 200 years

b. A house-elf's allegiance is foremost to its house (rather than to the inhabitants of the house)

c. House-elves cannot be ordered to kill themselves

d. House-elf magic is sufficiently powerful to override wizards' enchantments

e. House-elves breed infrequently and then only with their masters' permission

So from this we have to deduce which one is FALSE.

A is hard to tell but we do see many generations of House-Elves lining the wall of 12 grimmauld place the time line seems to be 150-250 years for these elves so a life expectancy of 200 years seems ill fitting but possible it could depend on external factors.

B is also tricky depending on how you determine it personally I think that their loyalty is primarily to the House-master that however could be due to their overiding loyalty to the House.

C we don't know if this is true they can and have been ordered to punish themselves in canon, so this is entirely possible although I think the reason we don't see any evidence of this in canon is due to the fact that wizarding families with house-elves generally want to keep their elves. We see one family disown their elf of their own accord (Barty Crouch Sr and Winky) this destroys Winky.

D well D is definitely true, we see it everywhere in canon. Hogwarts Anti-Apparation charms and also in Malfoy Manor Dungeon.

E With all the other information on House Elves in canon this fact seems to line up, they don't do anything without permission and you can imagine those pureblood families breeding with another pureblood familys' house elf for posterity.

The concensus on HP-Lexicon Commentary (When they did the test) is either A or B which I would also lend my (however limited) credibility to.

So it would seem that House Elves breed infrequently and with their masters permission, think of Purebreed dogs. Breed them once a generation for your next house elf, perhaps the babies stay with the mother or perhaps the baby just goes with the new master family and is raised by their current house elf.