You're asking questions that do not have solid answers. If the battery matches the output of the OEM battery then it should work. If the battery does not match the output then performance will suffer and it can lead to unexpected shutdowns.
Even here in California, I've known people who pay $ for battery replacements at malls. Even from the same kiosk, experience is wildly variable. Some batteries died completely within half a year, some bloated and popped off screens, and a few others operated normally. More often than not, you get what you pay for - I've seen more issues than not.
If I had the ability I'd try to go name brand as much as possible. Like iFixit or something like that - for an old device. At least you know the success rate would be higher.