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C3P0 is a protocol droid that seems to be used mainly for translations. Anakin said he built it to help his mother do her work.
What use would a protocal droid be to a slave?
(Please note that this is not a question on how he managed it, merely why he bothered).
CANON: In the Revenge of the Sith novelization by Matthew Stover, when he offers C-3PO to Padme, Anakin says he built C-3PO to be his friend since he didn't have many friends as a child.
Without anything of his own to give except his love, all he could bring her was a friend.
"I didn't have many friends when I was a kid," he'd told her, "So I built one."
And C-3PO had shuffled in behind him, gleaming as though he'd been plated with solid gold.
Padme had lit up, her eyes gleaming, but she had at first tried to protest. "I can't accept him," she said. "I know how much he means to you."
- Revenge of the Sith p. 113
In The Phantom Menace, back when he barely knew Padme, Anakin claims to have built C-3PO to help his mother. However, this could simply have been his justification he provided adults. After creeping on getting to know, falling in love with, and marrying Padme, he finally reveals that his personal motivation for building C-3PO was actually to fashion himself a friend. His personal reason for building him was to stave off loneliness. Any help C-3PO would be able to provide Shmi was likely just an added bonus.
While one of C3PO's primary abilities is translation, as a protocol droid he would be capable of many additional functions. For example, a protocol droid is seen serving drinks to Qui Gon and obi Wan in episode 1.
With that in mind, I had always assumed that the original intent behind Anakin building C3PO was to assist with chores around the house. As a slave, I would imagine that Shmi Skywalker typically worked long hours doing hard, menial work such as cooking, cleaning, etc and likely was often very tired and not wanting to have to do all the same activities when getting home. So C3PO would have taken care of all that for her.
Anakin was a mechanical geek. He assembled C3PO for the same reason some car geeks restore antique cars, or computer geeks upgrade ancient PCs - it's just how they express themselves and what their hobby is.
Anakin saw a cool droid in a junk heap, and it was a Project Worth Exploring.
He probably didn't come by all THAT many almost-functioning droids in the junk that he could afford to be picky.
Maybe part of her work is buying supplies at the markets. So, given that they live on a world where most of the demographics aren't human, she would need to know how to communicate (haggle) with the buyers and sellers.
"I didn't have many friends when I was a kid, so I built one."
