I understand your matter, unfortunately there is no general rule in French which can help us to distinguish between "feminine singular" adjectives and "masculin singular" with "e" at the end, but for sure you’ll never find a case of an adjective with an extra "ee".

The common rule if you have a "masculin singular" adjective without "e" at the end you have to add one for its "feminin singular" like :

"noir" "noire"

but it’s not a general rule as you can have the following case, which doesn’t follow this rule:

"blanc" "blanche"

For 1/, you are correct : ée is frequent in the feminine singular, but you’ll never find ee at the end of an adjective ; some end with e even in the masculine singular, but will have the same ending in the feminine form. Actually, I can’t think of any french word with a double e anywhere in it.

2/ is not so simple. As others have answered, there is no absolute rule to guess the masculine form of an adjective you don’t know given its feminine form. Most often it is based on pronunciation : if the final consonant is pronounced even in the masculine form, it requires a mute e. I’m afraid this requires knowing how the masculine form is pronounced though, and it’s not self-evident in many cases, as the pronunciation can change a lot between the two genders (e.g sain [sɛ̃] -> saine [sɛn]).

Some consonants are integrated with vowels and become muted (an is pronounced [ɑ̃], the n disappears), some are often muted in the end of words (s, t, sometimes d) and some aren’t muted but don’t require a mute e (l and r being the most common). But basically, ending a word with a consonant other than d, l, n, r, s or t is very unusual, most cases will require a mute e. Apart from these , you should be safe assuming that if the feminine singular ends with a “normal” consonant + e, the masculine singular will take an e too.

Do keep in mind, though, that French is quite an irregular language and that no rule of thumb will give reliable results : your dictionary remains your best friend.