Everything was fine until Saturday, when I suddenly started having trouble signing in. Takes a few tries.
If I get through that I get stuck at requesting character load.
Or get stuck when I try to change a zone.
Are you getting any specific error when you try logging in?
As for the loading screens causing you to get stuck changing zones, there is currently an issue we are aware of and detailed in the thread here. You can find more information in that discussion.
Error 301 indicates a connection issue where the game client was not able to connect to the server properly. A connection issue can also cause problems such as requesting character load. If you've not done so, please go through the connection troubleshooting found here. If these steps do not help, you should open a support ticket to have this further investigated.