OD&D is in essence the original red box or basic set series that ended with the Immortal boxed set and was largely based in Mystara.2. Are OD&D and 1st the same thing? What are the core book(s) to play called?
Original d&d had dwarves, elves and halflings as actual classes as well as races there was an option called Foresters that allowed humans to duplicate the elf class so they could both fight and cast spells with the same restrictions as elves.3. which one of these two had non-human races as classes? both?
From 1e onwards races and classes were kept separate.
No where near the gulf that separates 3rd edition from 4th edition, it was much more intended as an improvement on the previous edition than a completely different game.4. Are 1st and second edition very dramatically different? like 3rd and 4th were?
Original d&d will have the second highest chance of TPK but thats because until your characters have gone up a few levels practically anything can kill them even the domestic house cat!5. Can anyone give me a general feel or idea about these systems to help me decide if I'd like them?
First edition has a lot of instant death or save or die effects but whilst it introduces alot of new options such as psionics they aren't key to the game.
Second edition introduced skills and weapon proficiencies I believe 1e actually had a system where you could generate what social class you were and what skills your family line of work would allow.
Third actually allowed those other races to go for classes previously not allowed such as clerics or arcane spellcasters for instance, 3.5 merely altered a few bit and pieces that was assumed wrong with 3.0.
Fourth is a completely different game with power cards, encounter abilities and whilst not bad, you need to keepo an eye on what books are allowed a similar problem faced by 2e and 3e where the splatbooks could easily ruin your game if you weren't careful.
Pathfinder, well about the only bad thing is that the core rulebook is heavy and whilst the others editions had this split into three books this comprised the ph and dmg and has alot more options some of which makes sense but ultimately its up to you just how much you want to carry to your game.
If you game at home then you have no problem if you have a laptop, tablet computer, etc the pdf's similarly reduce what you need to carry.
Original d&d boxed sets come in basic (1st-3rd), expert (5th to 10th I think), companion (11th to 20th, I could be wrong), master (20th to 36th) and immortals (demi-god+) so you'd only need the boxed sets that cover your players' levels.
1e is three books basically the player handbook, the dungeon master's guide and the monster manual any more is up to you.
2e is the same as above as is 3e, 3.5 and 4e although with 4e you'll need to bring power cards or print them out so you can use them properly.
Pathfinder you'll need the core rulebook and at least the bestiary unless you for the Pathfinder boxed set which I believe covers the fighter, rogue, cleric and wizard up to 5th level and has everything you need to run if those classes are enough for your players.
Hope that helps.