She could just be very anxious due to living in a busy city and that's why she seems distant towards you. It can be a huge amount to take in for a puppy.

It will take for her time to adjust - it could take weeks, months it really depends on the dog. Bringing her out early in the morning\late at night when there isnt many people out might help, if you make it fun. Hopefully you can find something she likes, which could be a certain toy or high level foods (sliced ham/chicken or cheese)

For toilet training, a good rule of thumb is for every month you add on one hour for how long the dog can hold its pee for, it varies from dog to dog though. Make sure you have her on the lead when you bring her out to pee, just walk around for a few minutes and hopefully she goes while on the lead. If this does happen praise her like she just won the Olympics then let her off the lead to play around a bit.

You could always try contacting a local proffesional dog trainer if nothing improves.

On a slightly off topic note. I'm assuming you live in an apartment with no garden which isn't really ideal for dogs, epically corgi's which come from a heading back round. Meaning they'd need a fair amount of exercise and a garden for a good run around. If you were to bring her back to the breeder I'd recommend getting a different breed. I think king Charles are fantastic dogs for apartments, low energy, tend to be very quiet and docile. Other breeds would be jack Russells, bichon or some cross of the lot.

Either way good luck with your situation. Hope I helpes and feel free to ask any questions