A lot of good info being shared in this thread. Just want to add a few observations of my own.
1) During my first session, the players met a dwarf merchant on the road whose cart had been attacked and broken by a beast, and gave a poor description of the beast.
This is a cool interaction, but it creates an odd tension at most game tables.
In RPGs, you can imagine the text of the adventure as 'what's really going on', or as a sort of Platonic reality underlying the descriptions being given to the players. One thing that players will assume, especially when making skill checks to learn information, is that a successful check basically gives them information explicitly related to that underlying reality of the adventure.
But what if the information the characters have available to them is flawed in some way? If the dwarf had never seen an auroch before, perhaps it was describing a different creature it was familiar with, but trying to distinguish that it wasn't really that creature. Does a successful check reveal clues about the actual creature, or about the creature the dwarf is actually describing?
This kind of goes back to Robus and Iserith's discussion about determining just what it is that a skill check will do in the game -- but with the added wrinkle that you might not actually be giving out the information that your players' metagame knowledge is assuming you're giving out. To balance this, try to be explicit about what information you are providing ("What the dwarf describes sounds to you like an Underdark creature, but he seems adamant that such a creature could not exist above ground.")
I agree with Umbran that players and GMs are not necessarily great at conducting investigation scenes, and erring on the side of giving out more information can be helpful in keeping the adventure moving. But agreeing with that doesn't mean that players are justified in believing that a high enough die roll lets them effectively read your adventure notes -- you as GM have to decide what information is available, and how, and then adapt to how your players react to the information they receive as they try to interpret it.
2) My players stumbled across a clearing where a Green Hag and some Pixies had been the previous day, and my party's Warlock cast detect magic. I described the magic residue he found as being arcane magic, but I'm not entirely sure how to determine which type of magic to tell the party when they cast detect magic on an area.
Here's an area where deciding what information is available can be of help -- the idea of 'types of magic' in terms of spell schools really only applies to spells, not to magical creatures. Yet the creature type (fey, undead, fiend, etc.) can make for a decent alternative to a spell school. It seems to me that describing the residue your warlock found as 'a strange mix of light and dark fey-like energies' gives just as much useful information, if not more useful info, then trying to figure out if a green hag has a different spell school than a pixie. You can 'gate' this information behind an Arcana check if you like, with the idea that the Warlock wouldn't have even gotten the check without the spell, or you can rule that the warlock could have attempted an Arcana check without the spell simply by examining the residue, but that the spell simply obviates the need for a check.
This kind of simulates a mechanic from the GUMSHOE system that I rather like for this sort of thing; skills in GUMSHOE also grant a 'pool' of investigation points, which can be spent on a check rather than rolling a die. The more points are spent, the more information is found, up to the maximum the GM decides is available from that information source. Similarly, in D&D and similar games, spells or other expendable resources can be considered a 'pool' of sorts -- expending a spell slot is a much more significant indicator of effort than simply requesting a skill check, so more information should be available, if the spell is one that would be useful in the investigation. (Note that this also opens up the possibility that a detect magic ritual is not as effective in an investigation as the actual spell, since the ritual doesn't reflect a similar expenditure of resources. Some will balk at this, as the D&D rules don't make a distinction between using a spell as a ritual and not, so if you do plan to do this, probably run it by your players first so they're aware of when they might be able to get more information from an actual spellcast rather than a ritual cast.)
3) With the point our first session ended, our party is about to stumble onto a battle-scene where the battle has already ended several days ago, and one side in the battle had ogre zombies and elf zombies, among other things. When my party inspects the battle scene, should they be able to tell that these had been zombies, or should they simply see ogre corpses and elf corpses?
Again, I'd say it depends how much they investigate. If they simply pass over the battlefield, the corpses might not look all that different, especially if there were actual ogres or elves fighting as well as the zombies. Should they stop to investigate, there are already plenty of good examples in the thread above about the kinds of information you can provide, based on character background, proficiency in Medicine, or whatever other character feature seems relevant to you, including a skill check.
The main thing to keep in mind, though, is that if a piece of information is really significant, in that without it the group doesn't know how to continue the adventure, that piece of information should be as easy for the characters to discover as possible. Information that's simply 'good to know' or that makes the character's jobs easier can be more challenging to discover, as the challenge justifies the reward of the additional lore or the easier time in the upcoming combat.
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Pauper