1) I'd assume, for lack of any indication to the contrary, that rangers have spell books just like normal magic-users (which also suggests the same Chance to Know and Min/Max Spells/Level rules apply to rangers) and that a mage would be able to read a ranger's spell books with use of a read magic spell. I believe this was confirmed once upon a time in a Dragon Sage Advice column (though the Sage Advice was a dubious source -- often making stuff up and occasionally directly contradicting the rules in the books -- and shouldn't ever be taken as gospel).
2) Since the PH specifically states that rangers can't use magic-user scrolls, I wouldn't allow it, even if the ranger knows read magic. Knowing RM would only allow the ranger to read and copy spells out of other mages' spell books.
3) Again, for lack of anything to the contrary, I'd assume rangers are able to choose their druid spells in the same way druids do. Note, however, that the example of Otis in TOEE suggests rangers don't get bonus druid spells for high Wisdom (Otis is listed with only 2 druid spells, not the 4 he would have based on his Wis score).
PS: I think the 2E ranger was mostly based on people's 1E house rules and a desire to broaden and "genericize" the class, making it more of an all-purpose "wilderness scout" and less of a specific Tolkien homage. I'd always assumed the two-weapon fighting ability came from Drizzt in R.A. Salvatore's novel The Crystal Shard (published in Jan. 1988), but someone in another thread recently mentioned hearing from an authoritative source (either Salvatore himself or someone who worked for TSR at the time) that it was actually the other way around -- that Drizzt fought with two weapons because Salvatore was told in advance that rangers were going to have that ability in 2E AD&D, so who knows?
PS PS: You're probabsly mistaken, thinking of the guy who created the original illusionist (Peter Aronson, who's also posted here at least a couple times). AFAIK the creator of the ranger (Joe Fischer) hasn't ever posted at DF, though I could be wrong...
2) Since the PH specifically states that rangers can't use magic-user scrolls, I wouldn't allow it, even if the ranger knows read magic. Knowing RM would only allow the ranger to read and copy spells out of other mages' spell books.
3) Again, for lack of anything to the contrary, I'd assume rangers are able to choose their druid spells in the same way druids do. Note, however, that the example of Otis in TOEE suggests rangers don't get bonus druid spells for high Wisdom (Otis is listed with only 2 druid spells, not the 4 he would have based on his Wis score).
PS: I think the 2E ranger was mostly based on people's 1E house rules and a desire to broaden and "genericize" the class, making it more of an all-purpose "wilderness scout" and less of a specific Tolkien homage. I'd always assumed the two-weapon fighting ability came from Drizzt in R.A. Salvatore's novel The Crystal Shard (published in Jan. 1988), but someone in another thread recently mentioned hearing from an authoritative source (either Salvatore himself or someone who worked for TSR at the time) that it was actually the other way around -- that Drizzt fought with two weapons because Salvatore was told in advance that rangers were going to have that ability in 2E AD&D, so who knows?
PS PS: You're probabsly mistaken, thinking of the guy who created the original illusionist (Peter Aronson, who's also posted here at least a couple times). AFAIK the creator of the ranger (Joe Fischer) hasn't ever posted at DF, though I could be wrong...
Oh your right, that was the illusionist. 
