Etymology
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medico- 

word-forming element meaning "of or pertaining to medical science; from a medical standpoint; pertaining to medicine and," used as a combining form of Latin medicus "physician; healing" (from PIE root *med- "take appropriate measures").

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-ae 
occasional plural suffix of words ending in -a (see a- (1)), most of which, in English, are from Latin nominative fem. singular nouns (or Greek ones brought up through Latin), which in Latin form their plurals in -ae. But plurals in native -s were established early in English for many of them (such as idea, arena) and many have crossed over since. Now it is not possible to insist on purity one way or the other without breeding monsters.
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-ster 

Old English -istre, from Proto-Germanic *-istrijon, feminine agent suffix used as the equivalent of masculine -ere (see -er (1)). Also used in Middle English to form nouns of action (meaning "a person who ...") without regard for gender.

The genderless agent noun use apparently was a broader application of the original feminine suffix, beginning in the north of England, but linguists disagree over whether this indicates female domination of weaving and baking trades, as represented in surnames such as Webster, Baxter, Brewster, etc. (though spinster probably carries an originally female ending). Also whitester "one who bleaches cloth;" kempster (c. 1400; Halliwell has it as kembster) "woman who cleans wool." Chaucer ("Merchant's Tale") has chidester "an angry woman." In Modern English, the suffix has been productive in forming derivative nouns (gamester, punster, rodster "angler," etc.).

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-er (1)

English agent noun ending, corresponding to Latin -or. In native words it represents Old English -ere (Old Northumbrian also -are) "man who has to do with," from Proto-Germanic *-ari (cognates: German -er, Swedish -are, Danish -ere), from Proto-Germanic *-arjoz. Some believe this root is identical with, and perhaps a borrowing of, Latin -arius (see -ary).

Generally used with native Germanic words. In words of Latin origin, verbs derived from past participle stems of Latin ones (including most verbs in -ate) usually take the Latin ending -or, as do Latin verbs that passed through French (such as governor); but there are many exceptions (eraser, laborer, promoter, deserter; sailor, bachelor), some of which were conformed from Latin to English in late Middle English.

The use of -or and -ee in legal language (such as lessor/lessee) to distinguish actors and recipients of action has given the -or ending a tinge of professionalism, and this makes it useful in doubling words that have a professional and a non-professional sense (such as advisor/adviser, conductor/conducter, incubator/incubater, elevator/elevater).

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-re 

word-ending that sometimes distinguish British from American English. In the U.S., the change from -re to -er (to match pronunciation) in words such as fibre, centre, theatre began in late 18c. and became standard there over the next 25 years at the urging of Noah Webster (the 1804 edition of his speller, and especially his 1806 dictionary). The -re spelling, like -our, however, had the authority of Johnson's dictionary behind it and was unmoved in Britain, where it came to be a point of national pride, contra the Yankees.

Despite Webster's efforts, -re was retained in words with -c- or -g- (such as ogre, acre, the latter of which Webster insisted to the end of his days ought to be aker, and it was so printed in editions of the dictionary during his lifetime). The -re spelling generally is more justified by conservative etymology, based on French antecedents. It is met today in the U.S. only in Theatre as an element in the proper names of entertainment showplaces, where it is perhaps felt to inspire a perception of bon ton.

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-able 

common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro-, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).

A living element in English, used in new formations from either Latin or native words (readable, bearable) and also with nouns (objectionable, peaceable). Sometimes with an active signification (suitable, capable), sometimes of neutral signification (durable, conformable). It has become very elastic in meaning, as in a reliable witness, a playable foul ball, perishable goods. A 17c. writer has cadaverable "mortal."

To take a single example in detail, no-one but a competent philologist can tell whether reasonable comes from the verb or the noun reason, nor whether its original sense was that can be reasoned out, or that can reason, or that can be reasoned with, or that has reason, or that listens to reason, or that is consistent with reason; the ordinary man knows only that it can now mean any of these, & justifiably bases on these & similar facts a generous view of the termination's capabilities; credible meaning for him worthy of credence, why should not reliable & dependable mean worthy of reliance & dependence? [Fowler]

In Latin, -abilis and -ibilis depended on the inflectional vowel of the verb. Hence the variant form -ible in Old French, Spanish, English. In English, -able tends to be used with native (and other non-Latin) words, -ible with words of obvious Latin origin (but there are exceptions). The Latin suffix is not etymologically connected with able, but it long has been popularly associated with it, and this probably has contributed to its vigor as a living suffix.

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