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There is only one location that I am sure you can find an Abra, and the Pokeradar is not needed, but it will help, considering Abra is a rare encounter. You need to go to Route 8, and I would suggest you use the Pokeradar, which will be a pain, considering how little grass there is, but the alternative is walking back and forth in the same patch of grass until you finally see one, which would likely take a lot longer.

Regarding Shinies, I've never seen one, but I'm sure they exist. After all, it seems every Gym Leader has one, so you getting one yourself shouldn't be impossible. Hell, Purple flat out tells you that you have a better chance of catching a Shiny when you use the Pokeradar, though, as we all know, there are few places where there's a really good pokemon and enough grass to reliably use the Pokeradar. Basically... Good luck.