What did Uncle Owen want with an R2 unit?
At the beginning of Episode IV, Luke and Uncle Owen purchase C-3PO and R2-D2 from the Jawas. Well, whenever Uncle Owen talks with 3PO he mentions that he needs a droid that can understand the binary language of moisture vaporators (along with Bocce), but it's never mentioned what purpose R2 would serve...
Why would a Tatooine moisture farmer be in need of an astromech droid?
R2 units were known for their abilities of diagnostics and repairs. That would be important to anyone working with any type of machinery.
This is never expressly stated anywhere in any movie, and even the scene where R2 was purchased never really stated what Owen wanted with it.
However, this information is apparent by watching the overall original trilogy and seeing what R2's strengths and usage were.
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How did Uncle Owen not recognize R2-D2?Owen never hears his name in ANH. And as others have said, Owen is not likely to recognize him anyway, as he is just another protocol droid. Owen has very little contact or time spent with R2 in AOTC, and again, he doesn't hear his name in ANH. And like C-3PO, R2 is also just another astromech droid.
Is Owen older than Anakin?Yeah, Anakin was born in 41 BBY and Owen in 52 BBY so when the twins were born Anakin was in his 20s and Owen in his 30s.
Why did Owen adopt Luke?In 19 BBY, Beru convinced Owen to adopt Anakin's son, Luke Skywalker, as Anakin had turned to the dark side and become the infamous Darth Vader. Owen and Beru raised their nephew as well as they could, and Owen instilled into Luke the values of his own childhood.
Is R5-D4 an R2 unit?This seems to be in line with the non-canon explanation from "Skippy the Jedi Droid". Luke refers to R5-D4 as an "R2 unit".
Star Wars: A New Hope - Luke Skywalker Meets R2-D2 and C-3PO [CLIP] | TNT
More answers regarding what did Uncle Owen want with an R2 unit?
To diagnose and repair this vehicle, perhaps?
I mean, they have this kind of vehicles that may need repair, therefore the need of an R2 unit