Do you find it to be well, 'druidy'?
Mostly. If you ignore the possibility of "our druids are different", RL druids are usually people who supposedly use the magic contained within plants and animals in order to cause different effects. Sometimes these effects are distilled for personal use, sometimes those things are manipulated within their original "containers" in order to get certain effects (usually through the use of those distilled effects). Commonly they also become a combination with shamen type spiritualists (with all the authority that comes with it) or deep-immersion hermits (with the identification with nature that goes with that); but this is not wholly necessary to be a "druid". The religious aspect of it is more difficult to define as they tend to be more secretive than other groups and most secondary knowledge is about the effects, since those are verifiable and more likely to be written down by outside observers (so I can't really comment on how consistent those particular beliefs are). The "end game" state of a druid is similar to a blood mage, distilling power from the corpses of animals or sometimes humans in order to gain greater effect than can be otherwise gained.
So, quite honestly, the druid system is very close to real life (assuming that you believe that RL druids are actually doing anything). Just add a potion of "charm animal" and replace the runes with potion effects that do the same thing, and there you go.
Do you feel that the current druid/alchemy system is equivalent to, greater than or less than the mage magic system despite their respective differences?
Both get a lot of versatility in their spells whereas the druid/alchemist's power seems less because everyone has access to it (assuming that they have the money to buy potions from someone who is a druid). The areas where mages outshine druids/alchemists are their teleport spell, utility battle spells (stun, wall, whirlwind), and the fact that they don't have to spend money on every casting (they use mana). Druids have stat enhancers, non-combat utility potions (language potions, transformation potions), the ability to help allies without having to be physically present (passing out potions), the ability to make money by selling potions, and the possibility of a nearly endless supply of "magic" not hindered by mana (they buy bottles/herbs/gem dust). Druids are also not restricted by "necessary" stats and have an easier time skilling (more on that later). Both have attack spells (with them topping out similarly), healing (though mages are probably better at it), and can be interrupted (the reason why mage healing beats out druid healing, but also the reason why druid attack spells very well may beat out the higher end mage attack spells in some cases).
So then the biggest two things that separate them is that anyone can use a druid's potions, and druids don't have the same stat and leveling requirements. The first makes a druid seem unbelievably weak because anyone (even a mage) has the ability to have access to the majority of a druid's power. The argument there is, "why build a druid/alchemist when you can just build a mage and buy the potions?" The counterargument is that druids with stock are hard to find and you are better off just making your own and having as much as you want. The lack of stat requirements and having only one skill to raise is what more than makes up for that weakness (Herb Lore being the skill, Alchemy only needs to be high enough to check the quality of herbs). For the vast majority of mages (even battle mages) a similarly experienced warrior can wipe the floor with them if they get close. A warrior needs to build 4 skills while a battle mage needs to raise the same 4 plus 3 or 4 more skills that raise more slowly while a battle alchemist needs to raise only 5 skills; this means that "end game build" is not the right place to look for an even comparison. The stat difference means that a battle druid generally has a MINIMUM of 20 more stat points to put into their physical stats than a battle mage, assuming that they bottom out their "unnecessary" stats and the mage has bottomed out their mage stats to the minimum required to learn magic (using human numbers). If a mage doesn't bottom out those stats, than the difference is much bigger. How big a deal is 20 extra stat points? Out of a total of 84 total points, that is about a quarter; and out of the avalable ~58 points (once minum stats are taken into consideration), that is about a third of your total points that you have to spend. And that is assuming that the mage optimizes for battle rather than for casting ability, which is a choice that a Druid/Alchemist does not have to make.
I'm going to have to say that druids are more powerful, an obvious comparison. Especially since the high level skilling process for mages is so difficult that maxed mages are pretty rare.
Do you feel that the druid/alchemy system is a good match for potential druid RP? does using it make you want to RP like a druid?
As answered above, it is a good match for a RL druid but not necessarily for a D&D druid (which is what most people think when they hear the term "druid"). D&D druids are basically mages with a nature specalization, improved familiar, and extra "polymorph self" spells.
As for the idea that the rules could force someone into playing a certain way, as it seem by the "want to RP like a druid" statement; that is something I take some issue with. Some characters using the mage system are "wizards" and some call themselves "shamans" and some have other terms for themselves. I don't believe that the system should force you to RP in ore way or another, because that is restricting to the one thing about this game that truly makes it fun. If you want to play a game where you are forced to be a nature lover simply because you use alchemy/druidity, than there are plenty of games where you can do that. But I would pleasantly ask you to not try to make this be one of them.
So, no, I don't think it makes me specifically want to RP like a druid, though that is a strong direction that it can take. But I believe that this lack of imposed direction is a good thing.
Lastly if you had some suggestions for the druid/alchemy system (different runes, new potions, different abilities) what would they be and why?
Give druids/alchemists an ability that makes their potions work better on themselves or other alchemists than it does on everyone else. This would add in some of the exclusivity that makes Mages appear so powerful despite the fact that Druids/alchemists are actually more powerful. Perhaps replace that one rune that supposedly transfers skill.
Do something about the stupidly high price of gem dust, it isn't even craftable.
Add in some variations on well used potions, such as bombs that are more easily used at point black range.