yeah i agree, download FileZilla and log in and all that bologna, delete everything on the server (make a backup if you wish) and just put on what you download from the Hexxit sight. this same thing worked for me.
a little tip before you play tho, make sure you go through all the files on the server to make sure everything is in them. I learned this the hard way.
the way i suggest putting files onto your FTP is one directory at a time (make sure server is stopped) then when you got all that loaded in, use the Hexxit.jar as your primary jar file NOT minecraft_server.jar
you may have to contact your hosting service to allow you access to a certian bukkit thing ((my server runs on craftbukkit 1.5 #2686) if that helps any), just tell them you want to run Hexxit, and they should enable it for you. EDIT: i read the other half of your post about the customer service, all i can say is find someone on there that knows what Hexxit is (unless everything works without their help)
if you are getting severe errors when the spawn is generating, just press the restart button, sometimes this fixes it.
Also the reason your map and damage indicators and TMI works is because for the most part they are client side, trust me the same thing happened to me.
Need anything else PM me.