Though I may not be able to play Kronos as much as I would've liked when it comes out, even if I didn't play it, not answering these questions with experienced facts would haunt me until I die. I played vanilla during its retail years and was part of a competitive raiding guild on the Draenor server, Horde side. My druid experience comes from a guild friend during that time, and my personal experience during my time as a druid on a vanilla private server, don't know if we're allowed to name drop here, but I heard nothing but good reviews on it before it died fairly recently. Though I had critiques, like mobs using their special mechanics at least 3 times more often, anyway.
"1. I heard the only "playable" spec is Resto. Is this true, or are there ways to play a tank druid too?"
Though I'm not surprised you heard this, it is very wrong, and I'll explain why
Bear Tank: The issue associated with bear tanks is the difficulty in becoming defense capped. Though still possible to do so, the stats sacrificed are not worth it. Bear tanks basically have to take a different approach, being high stam, armor, and agi/dodge. My tank had about 30+% dodge unbuffed/no consumables, before the p-server went to crap. Our guild UoS in retail vanilla had a bear tank, Herculees, who tanked all the time, whatever he wanted during raids without an issue, and it never halted progression.
Perks to bears: 1.Since you have no defensive abilities/buttons, all your time/rage is dedicated to threat, this being the case, yes, you do threat circles around other tanks. I never once had an issue out threating, or coming in after and getting threat over other tanks. Doesn't insult their skill, its just the layout provided. 2. Since agility is one of your 3(4, being dodge but agi contributes to that) stats you seek after, you have very high crit, which helps with threat and rage gen, rage gen can be a problem for tanks (especially when a priest bubbles you at the start and you cant get rage from taking damage), bears don't have this problem. 3. Resistance gear, when using resistance gear, many stats are sacrificed (shield block value, sb chance, defense, parry, dodge, etc.) however, druids don't sacrifice anywhere near as much as other tanks considering resistance gear has 2 of the three stats commonly sought after. Bears make great resistance tanks. 4. Ill stop at 4 because I hate making huge posts (and I know this will be one), but simple druid mechanics. I speak for my experience in ZG which is a great place to tank as a bear, Jindo polymorphs all the time, and you should just tank him with a bear, period. Also (though I don't remember if we tried this in retail) the spider boss's web mechanic where you usually have to tanks (one to catch her) could be shapeshifted out of (on the p-server I was on) making her a 1 tank pony. There are many perks to bear tanks that are commonly over looked, but the 1 true requirement to playing, is taking the time to get all your "pre-raid best in slot gear," consumables, enchants, etc. Just do your work as you should before raiding and you'll be tanking fine. I was told I was fine to heal, sometimes easier when doing encounters, remember, healers know more about what they're doing now too. There are some perks to private servers too haha.
Balance ("oomkin"): Though my experience is less in this field, I know all of the top raiding guild on my retail vanilla server had at least one, sometimes more. The problem associated with this class/spec, is the lack of attention before trying to jump into raids. This meaning, no pre-raid BiS, consumables, enchants, etc. Whereas if a mage/lock did this and sucked at damage, they at worst got "L2P" "scrub" "do better" insults and whatnot. If a balance druid did this they received many "you're the wrong spec" "oomkins suck" "go respect to resto now." The problem being, nobody got to see the cases where balance was done right. Sorry to burst your indoctrinated forum knowledge guys, but a proper raiding balance druid would pull agro before going oom. The term Oomkins came from inexperienced played (mainly in pvp) who didn't know how to react when pressured and just spammed their instant cast (moonfire) which is terrible on mana. Though no locks/mages were gonna defend balance in anyway shape or form, well, because that's gear competition.
Cat ("kiddy dps"): Im sorry, I have no experience with this, nor can I defend it. I can only defend a alliance player (in pvp) "Cptoblivious" on Draenor who could kill clothies really fast as cat and not die as a bear. talking hour+ long stalemates in wsg. Other than that, I can't say anything for cats. Though, maybe this could be your chance to experiment with that aspect and see what can be done.
"2. Is it possible to have a hybrid specc? Like feral/heal or balance/tank or even all three specs? (I remember, back in Cata it was possible to play bear/cat pretty good)"
These "hybrid" spec's usually shine in pvp and that covers it. I wouldn't try them in raiding. Instances might be fun with them.
"3. How is the solo-content (leveling/questing) as a druid? And would it be possible to make it through as a resto?"
I've only leveled a druid twice, but I hate early levels (namely 1-10), I know, very small sections, but I mean its sooooooo boring as a druid. Even after that its still boring imo. Though I never even leveled cat, I still did bear just cause of ease. Made doing group quests very easy though, cause I could solo them. However, I don't have much input for this, just to avoid resto leveling of ANY kind in vanilla wow, unless you have a buddy leveling with you, then go right ahead.
"4. Is there just THE ONE skilltree for each specc, or are there some more?"
This to me seems a lot like question 2, but I can see the reason for asking. In most specs and cases, "THE ONE" you find online or however, has usually had some research/experience behind it and tends to suit the role the best. Though for your own preferences, minor tweeks can help. This being the case, experiment as you see fit and you might find something better. However, imo, with the work already done, id stick with the ones you find (with maybe minor tweeks)
Sorry for the long post, just wanted to give some experienced insight to a long distorted topic (not saying here, but since the games release and throughout forums). Really hope the guy who asked the initial questions sees this before giving up on druid playstyles lol. Though the real answer to all of those questions is a very simple, Play whatever you think you'll have the most fun with, the style you like, its a game. You might find some trouble getting into raids as the choice you want, but I'm hoping Kronos will be filled with experienced players who know more than the forum misconceptions.