Can't update themes, plugins. Can't delete files.

I’m having lots of problems with wordpress lately. They all seem somewhat related to permissions and access, but I can’t figure out the sources of the problems:

1. I can’t update plugins. When I try to update one of them, I get the error “Could not remove the old plugin. Plugin update failed.” If I manually delete the plugin using my FTP client or the file manager from my host, then I can install it fresh, but obviously this is not ideal because I lose all my settings and it is cumbersome.

2. I can’t update themes. When I try to update one of them, I get the error “Could not remove the old theme. Theme update failed.” I can manually delete the files for the themes from my FTP client, but I can’t delete the theme folders themselves no matter what I try. Permission are set to 755 on the folders I am trying to delete, though I’ve tried many other combinations.

My host, bluehost, said that “something within wordpress-admin is preventing it.” but didn’t elaborate, explained they weren’t web developers, and then disconnected me from our chat (twice).

3. I often get the message “Briefly unavailable for scheduled maintenance. Check back in a minute.” when I try to access my site. I realize I can get rid of this my deleting the .maintenance file, but it seems like I shouldn’t have to do this.

So at this point, I can reinstall the plugins even though it will be extremely tedious (and I have no idea if I’ll be able to easily update them in the future) and I am using a theme I don’t particularly like because I can’t install the one I do like (can’t delete the folders and wordpress can’t update it).

My site is http://www.travelorders.com. WordPress version 3.8.

Any advice?