Thank you, that solved a half of my problem. I still cannot connect to the online resources, but I managed to open maps through ArcCatalog. However, since I still cannot connect to the online resources, some tools just failed to achieve, such as projecting my map or running regression analysis. My proxy server test is okay. It was my Network Latency Test - Undetermined ; Network Route Test - Failed. Both reasons are unknown.
I'm sending an email to my school's IT, but if you or anyone know any strategies, please let me know. Thank you!