Hi, and welcome

followers & horses: they don't ride a horse themselves, unless you use a mod. When will they accompany you again? No idea, since I never use horses, sry.
date & game-time won't matter, regarding quests that you have yet to start....quests start when you trigger certain events (like talking to someone in particular). Even if you "pause" a running quest (by leaving halfway, for example), it will stay active, and continue when you pick it up again, even if that's weeks of ingame-time later.
You can enable or disable quest-markers in your ingame Journal menu...it will only disable the marker on your HUD compass, NOT any running quests.
If you for example are following a person to a location, and he/she's waiting for you at a cave-entrance, you can backoff and go do something else, and come back weeks later, and still find that person waiting for you there, to continue the quest.
You can try to get a dragon's attention, by shouting at it, or by hitting it with arrows or (long-range) spells...sometimes it works, sometimes the dragon will ingnore you and fly away.
Alchemy: you can search for recepies at a http://www.uesp.net/wiki/Skyrim:Skyrim, allthoug that's a bit like cheating. Or you can try to combine ingredients of which you already know the 1st effect, based on guesswork (for example, you can be sure to get more interesting effects from deathbell or nirnroot, because they are interesting plants lol).
If you worry about messing up quests, there is a mod which gives a warning that the quest in question is related to certain other quest-lines....unfortunately, I can't give you a link, because the mod file is currently hidden by the author (probably because he/she's about to update it)....but give it a day or 2, and then search for a mod called "DungeonQuestAwareness".
Some quests though, require you to find a certain item...but without the actual quest started, you may still encounter those items. They usually have a name that sticks out (like the name of the previous owner).
Quest-items can't be dropped from you inventory, and stay there untill you finish the related quest. But in case you worry about the weight of a quest-item: don't let the game fool you, regardless of any weight-number in your inventory, their weight is 0
So just let it stay in your inventory, and when times comes, you will get a message from the game, that you've just fullfilled some quest's requirement (for example, get item X for Person Y at location Z), and you can go and finish the quest quickly...like when you already visited that location, and found the item, but only now meet and talk to the person who wants it.
p.s. I hope you're on PC, otherwise, ignore my mod suggestions.
http://skyrim.nexusmods.com/index.php is your best source for mods...get the Nexus Mod Manager, it's a breeze to use.