Not usually. If an appendictis is treated with just antibiotics, it may improve but the chances of recurrent attacks is high. So, the appendix shoudl be removed surgically.
Yes, but.... Some people will respond to IV antibiotics in a hospital setting, however most people won't and we have no reliable way to predict who will get better and who will get (much) sicker. Therefore, in all but the most unusual circumstances, the benefit of surgery far outweighs the risk.