Percentages of meanings in an English dictionary
Solution 1:
The number of senses a dictionary reports depend a good deal on how much space it has and how long the lexicographers are allowed to parse the data. Typically, the more they look, the more they find. The Longman Dictionary of Contemporary English uses corpus data to sort its senses by frequency though they don't provide the sense frequency information. Interestingly, Adam Kilgarriff, who worked on the 3rd edition of the LDOCE points out that in almost all cases, the most frequent sense of a word is overwhelmingly so. Adam's website with a number of relevant papers is here.
Solution 2:
It really depends on the dictionary as to what order they are. Some group meanings logically, others chronologically, and most according to how "common" they are - but that commonness is usually subjective.
If you want word frequencies, you need a corpus, not a dictionary. Look at Google Books search, for example, if you want to know how frequently a word is used in a given phrase or part of speech. in theology, trying to get the meaning of a Greek word as it was used at the time the Bible was written, there are corpses of "Greek works at the time of the Bible". You'd want to differentiate that from, say, modern Greek, for the same reason you'd want to differentiate, say, slang from scientific research.
You need a corpus, because you need to define your total population of words, the denominator of your percentage. There simply too many words to get a frequency otherwise - even Google books, one of the largest publically accessible corpuses, indexes less than 10% of the books out there.
For more information on corpuses, you should check out Grammar Girl's podcast which recently did an episode on one by clicking here.
Unfortunately, this is going to be able to show you how a word is used, but semantic meaning is really tricky. You're best bet would be to isolate meaning by how its used. Since there is no standard on the various meanings of a word, you'd have to find a dictionary tied to a particular corpus. For theological work, you can often find tagged grammars that might get you what you want - but if you're looking for a more general purpose dictionary, I strongly suspect you'll be out of luck. Since knowing the exact percentage of a given use is such a specialized query, I doubt its worth anyone's time to compile an exhaustive list of several words tied to an arbitrary set of meanings. If you can narrow it to a single word (or several words), you can probably do your own, but I'd be amazed if the resource you want exists.