it depends. From what I know, a store credit card is considered the same as a bank card (for your credit history). At any point it is good to have around 2-3 such cards open. any more or less, and you risk being considered as not such a good credit risk
No , the credit score will not go down nor go up. Just stay the same. If you open a new account, you credit score will go done a little bite.
https://www.creditnotify.com
I used this service before, it is pretty good that they have "what if" feature. It shows your current score, and what your score will be if you do the "what if" such as open a new account, borrow money, ...
Best wish
I would think that the score would go up. Some factors which could lower your credit score would be having accounts with high debt to limit ratios (maxxed out credit) and multiple credit accounts. The thinking being you could always go out and add more debt.