Many questions...let's break them up.
1. Keeping links: Projects contain within them the raw data needed to re-establish the link if it isn't there. If you open an online project and the link fails to talk and then you choose to go offline, the option to discard the link is offered to allow you to remove the link information from the project and make it an offline only project.
2. When the CommServer validates a link at startup and finds it broken, it disables it. Any subsequent use of that link requires that it be re-enabled. That can happen a few different ways, but checking the box is one of them.
3. When you start DirectSoft with the PLC off, the link will be disabled by the CommServer which was unable to validate the link. Turning on the PLC and hitting "Retry" should work; I'm not sure why that didn't work for you.
4. A link is a named connection, to a specific type of PLC, using a specific protocol, at a specific address, on a specific port, with a specific configuration. You may use the same link in multiple programs, but changing any of the above settings constitutes a different link, and the system will regenerate them when the project is opened if it can't find the appropriate link. Certain things can be different, like the baud rate for instance, but critical things must match to be considered the same link. There are a number of PLC specific behaviors that are managed by the CommServer, which is why the link must be correct. Trying to use a DL240 link with a DL230, for instance, can result in unexpected, and unpleasant, behavior.
A little background: The CommServer, and its quirky use of links, was designed to provide high performance networking between multiple PLC's sharing a single RS422 port under Windows 3.1. Disabling broken links was critical to maintaining performance for everything on the network, as a broken anything in a co-operative multi-tasking environment had the potential to bring the entire system to its knees. In an effort to keep things crisp, we try to turn the lights off when no-one is home. Sorry about the confusion.
Since 1992 when the original design was completed, Windows has moved forward a bit and most networking is performed by Ethernet. Stated another way....much of the original design justification has changed. The CommServer has been updated multiple times to take advantage of true multi-tasking, but we still support old fashioned serial ports, and many people are still running RS422 between multiple controllers...so it will probably stay like it is for the forseeable future.
You can turn off the start up link checking (tech dudes, please chime in with specifics on that) and that will help the issue of what DirectSoft does at power up...but...we will probably continue to turn off links that don't work.
Probably haven't answered your questions very well, but it has been a nice walk down memory lane for me. It has been a long time since we did that work...