I can help you with some answers.
Vassal is a computer program, written in java, that allows you to 'mimic' a board game and play it online. At its core, it lets you add graphics for the board and pieces and gives you a facility to move those pieces around. You can play either online real time or pbem with Vassal storing a log of your moves so that your opponent can play back your turn.
So as to your questions, the answers are:
Yes, it can be. With CoH it's better to perform all of your activation and then let your opponent step through the log until he wants to react. He can then start a new log file with his reaction to send to you from where you can start a new activation (or continue with the current one if his reaction doesn't alter your action)
Yes, you can play in one sitting but don't have to.
You can save a game in progress to pick up later.
There are features in the module to roll dice and see the results. Some people don't trust the in game dice roller and prefer to use a dice server.
Yes everything is on screen and you can move your pieces and your opponent will see the movement either realtime or in a log file.
In the CoH module there are lots of automated features such as a LOS string and being able to hide pieces so that you can still see them, but your opponent can't. The in game text files cover these.
The website
www.vassalengine.org has a lot of info on getting started. It's also where you get the vassal software as well as the CoH module.