Well I found that I need to use file - close window instead of file - exit and that does as I desire. It's not a solution but I have become used to it.
And yes there is an adequate Firefox add-in similar to IE accelerators ... it's call
cleeki
Here is a list of the accelerator settings I added. To write your own, "[kw]" is the parameter cleeki replaces with your highlighted text when calling the site. The hardest part was often finding the favicon on the website. And supposedly you can import ie8 accelorators but I have yet to find a way to make this work. Note: I do not use the channel preview option so I have it set to the same as my Channel search URL.
Channel name/desc: Wikipedia
Channel Icon: http://www.cleeki.com/images/wikipedia16.png
Channel search URL: http://en.wikipedia.org/w/index.php?title=Special%3ASearch&search=[kw]
Channel name/desc: IMDB
Channel Icon: http://i.media-imdb.com/favicon.ico
Channel search URL: http://www.imdb.com/find?s=all&q=[kw]
Channel name/desc: Merriam Webster Dictionary
Channel Icon: http://www.merriam-webster.com/favicon.ico
Channel search URL: http://www.merriam-webster.com/dictionary/[kw]
Channel name/desc: Bing
Channel Icon: http://www.bing.com/s/wlflag.ico
Channel search URL: http://www.bing.com/search?q=[kw]
Channel name/desc: Yahoo!
Channel Icon: http://www.yahoo.com/favicon.ico
Channel search URL: http://search.yahoo.com/search?p=[kw]
Channel name/desc: cnet
Channel Icon: http://www.cnet.com/favicon.ico
Channel search URL: http://www.cnet.com/1770-5_1-0.html?query=[kw]
Channel name/desc: wolframalpha
Channel Icon: http://www27.wolframalpha.com/favicon.ico
Channel search URL: http://www27.wolframalpha.com/input/?i=[kw]