Well, until now I cannot see a solution that matches all 5 mandatory requirements...
But I think I'll give up searching - at least until someone post a best answer.
With the help of @avirk and testing translating other pages with mentioned tools, I re-analysed them and took some decisions...
Palliative Solution 1:
To use FlagFox add-on
In which cases?
For sites that not require authentication (HTTPS), form posting, scripts... So you can configure FlagFox to translate page at 1 mouse click on flag; you should do it once and every link pressed (with mentioned limitations) will access its translated page.
Why?
It does not support some scripts, form posts and HTTPS, so you can use that to navigate in sites like Wikipedia, news etc. (but you cannot edit wikis, post comments, share news on social networks...).
It matches requirements?
No at all (2.5 of 5 mandatory points):
1. Translate pages automatically after entering URL;
-> Unchecked.
2. Display of the page would be as in original language (links, images, flash
contents... would not be affected);
-> Checked partially: Inside HTTPS pages or pages that require some scripts, it would not show it as in normal navigation.
3. Linked pages must be also translated;
-> Checked: Well, since linked pages are not HTTPS or require some script or form posting, it will function perfectly! You must only mouse click once on first page.
4. Other browser operations must not be affected (e.g. posting forms,
downloading etc.).
-> Unchecked: As said in 2 and 3.
5. Firefox solution (I hate IE, Chrome, Opera, Safari and all others than
Firefox, but I accept also a general solution but that function on
Firefox).
-> Checked.
Palliative Solution 2:
To use Google Translator Script Bar
In which cases?
For sites that requires authentication (the cases that solution 1 does not cover).
Why?
It supports some scripts, form posts and HTTPS, but with that you must do that annoying thing to press bookmark on every new link pressed...
It matches requirements?
No at all (2.5 of 5 mandatory points):
1. Translate pages automatically after entering URL;
-> Unchecked.
2. Display of the page would be as in original language (links, images, flash
contents... would not be affected);
-> Checked: And it is so good!
3. Linked pages must be also translated;
-> Unchecked: :(
4. Other browser operations must not be affected (e.g. posting forms,
downloading etc.).
-> Checked partially: It launches some Google error messages for some downloads;
5. Firefox solution (I hate IE, Chrome, Opera, Safari and all others than
Firefox, but I accept also a general solution but that function on
Firefox).
-> Checked.
Summarizing:
- Palliative Solutions 1 and 2 can do the work well, but with some restrictions (and do not cover optional requirements);
- What would be a better solution (what matches requirements):
- An add-on (or something like that, GreaseMonkey perhaps), that uses Google Translator Script Bar (or similar) on every page, just inserting an URL on address bar and entering it, without the need of pressing a button after the page is already loaded;
- It would be nice to have in it a button to enable/disable toggle and some kind of blacklist/whitelist (= optional requirements mentioned).
Best Answer
Mozilla Labs has something called RecallNonkey that's being developed for this purpose. http://mozillalabs.com/prospector/2011/06/20/recallmonkey-finds-what-you-forget/
https://addons.mozilla.org/en-US/firefox/addon/prospector-recall-monkey/
This is a local search against the history entries in the places database and I don't believe it sends any information out there - it's still pretty new/experimental but I've been using it for a little while and it seems to work well.