All you need to install your e-Sword module is to enter your Email address and "Product Key" you received when you purchased the module. If you do not have that information, just click on the "Recover Product Key" button on the dialog that prompts for this information.
Updated to e-Sword 11.0 as these new resources are not compatible with any older versions of e-Sword.
Highlighting and marking is stored in character-based positioning. The introductions of the Pericope (section headings) obviously changes those positions. You can certainly turn off the pericope to realign the positions. Select "Options, Display Pericope" from the e-Sword menu to do so. If you decide you want to have the Pericope displayed, then you will have to update the highlighting and marking as needed when you encounter them.
Use the Download menu from *within* e-Sword. Check out the "Download" demo on the Training page.
If you are on a home network, then run the "Internet Options" applet in Control Panel. Click on the "Connections" tab, then click on the "LAN Settings" button. ONLY "Automatically detect settings" should be checked.
If you are on a work network, then select "Options, Proxy Settings" from the Downloader menu and enter your network requirements. (Your IT department will have that information.)
If you are still experiencing trouble, then it sounds like either an Internet filter or firewall (e.g. ZoneAlarm, etc.) is blocking e-Sword from accessing its server. You can temporarily disable these and see if that helps, and if so then you can add an exception for e-Sword to their settings.
You can delete a resource by selecting "Options, Resource" from the e-Sword menu. Right-click over the resource you want to remove, then choose the "Delete" popup menu item. Confirm, and it is gone.
Check out the "Views" demo on the Training page.
Those are Bookmarks. Right-click on one to set it to the currently active verse; left-click on one to go to its reference.
Copy the e-Sword *program* directory (typically "C:\Program Files (x86)\e-Sword\") onto the new PC as this will get your various modules transferred. You will still need to install e-Sword from its setup program to properly install the various system files, etc.
Also, you will want to copy the contents of your e-Sword *user* directory (typically "Libraries\Documents\My Documents\e-Sword\") to get your personal notes and other customizations transferred.