There are a bajilion addons for Firefox to download vids. You need more than one, as not all sites are supported by any addon. Most all support all video resolutions provided by the site, A few require you to pay for HD features I just pick another addon if that shows up as you don't need that crap.
Also you can use VLC as a player in a browser and use an export module in VLC to support odd ball sites the addons won't.
There are also web sites that will download vids from some sites addons don't work on. You will have to add your site username/password to the link you paste in the web page, lots of web pages show how to add the do the username/password in a link bit.
Another thing to note is not all addons work on all versions of Firefox. An addon can work on one version of Firefox and not on another. I use an older Firefox(USE Long term stable versions. Newest versions past 56 are crap. You need to enable legacy extensions.) and older addons mixed with newer. I update addons manually, updates often break addons. For instance I use an older ADBlockPlus with the new updated blocking rules, by the way ADBlockPlus has to do with video downloads as some sites put AD's in video breaking downloads(You will get chunks of video rather than full vids if AD's screw things up. Keep those rules updated. Addons can interfere with other addons, and order of loading of addons can matter. Status bar forever is your friend with lots of addons.
I do not endorse or recommend specific addins any more as too many asswipes report addins that work, making it harder to find good ones.
You pay for your vid you should be able to download it and watch in in high res off line, sites that try to block this should be bitched out and avoided if possible. Sites charge way too much money these days, One I want some pic sets and a few vids of the only two women they have I want wants $50.00 cripes, I'm hard pressed to find $10.00 these days and they want $50 but its been a couple of years and no one has posted them anywhere. I keep looking for the lottery but it seems to go to people who say "It won't change my life.", If your that rich why play?
Back to addons, also remember there is streaming video and inline/embedded video they are different and usually require separate addons to download properly. Streaming is usually in blocks that need put together, I downloaded one streamer that was over 200 pieces for a 9meg HD video clip crap, idiot at work is my guess.
Java, Flash, GL, RTC, SL, can get in the road of downloads (There is an addon to fix this.) I recommend having these off until you have to have them, most of the time you don't need these. You may need site specific addons to enable the video download plugin to work(Example Inst@ram addon to download inst@ vids with video download addins and picture downloaders.).
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Google(AD's over all else, sadly.), facebook(True EVIL.Indited for stealing from children and thats not the truly evil part.), twit***(Its already there TWIT.) are all enemies of the people!
OK Ok off the soap box but you look into these companies and you will find in the end they are servants of evil even if there moto is do no harm. Like so many Doctors these days who do the evil of the evil minions in our governments they don't understand what "Do no harm." Means.
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If there is a large request for it I mite do a post on how I deal with Firefox Addon problems. Things like "It always worked, what the hell happened?".
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Also something I recommend is hard drive swap racks, these are pretty cheap. Setup drives for web crap, etc. shut down swap drives, fire up away you go. Its hard to make a one browser for everything and if you do its often slower than you want.
Now you can do virtual machines, but these require blazing hardware, tons of ram and are hard for many to master. Swaping drives is way simpler.
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Anyway some ideas.