So it looks like tweaks more than a full blown different rules set, is this a correct assumption?
More or less. Optional material from later 1e rulebooks were added to "core" (biggest example are the proficiencies), while things like half-orcs, assassins, and monks were dropped. I've never noticed any real significant difference between the two rules, and my guess would be that 2e is easier to run than 1e with some of the more complicated bits removed (particularly with combat being streamlined).
Didn't they drop artifacts? The funny hat man has a good list. So you could use either rule set for Dragonlance.
Nope. Chapter 10 of the 2e DMG talks about artifacts, and gives a brief description of 3 as examples, IIRC they are the Hand and Eye of Vecna, the Rod of Seven Parts, and Heward's Mystical Organ. No powers are listed for any of them, instead the DM is encouraged to give the artifacts whatever abilities are needed for the campaign. The Book of Artifacts later updated several 1e artifacts and included a few more from the existing campaign worlds at the time it was published, it's mostly descriptive flavor text with recommended powers and methods of destruction for each artifact. The book also has several tables of powers grouped into categories for the DM to choose from, and IIRC, two of the tables weren't used for any of the standard artifacts in the book, but were included for anything the DM might create. In any case, the artifact tables and all the artifacts themselves were reprinted in the Encyclopedia Magica, so the Book of Artifacts later became somewhat obsolete.
I have a vague memory of how hit points were handled changing. Something along the lines of changing at what negative HP value death happens at, the exact details escape me ATM. It might have even removed negative hit points its been too many years...
It was an optional rule, if the DM wanted once a character hit 0 hp, he fell unconscious and lost 1 hp/round until hitting -10 and died or was healed with a spell or potion. A lot of DMs allowed the healing proficiency to stop the hp loss, but I don't remember if that was part of the rule or not.