Yeah he did, and when Barry was travelling to Earth-2 and caught glimpses of other universes, there was a brief shot of the 1990 version of The Flash (so basically that version of The Flash exists in this show in another universe which is a nice touch
).
Mark Hamill played the Trickster originally in the 1990 show too (and they used images of him from the 1990 version in the current show when referring to his crime spree from years ago).
And Tina McGee (that English scientist woman) was played by the same actress in the old show as well.
I really like how they keep making references to the older show, they really do have a great love for the whole Flash mythology.
About Eddie, yeah I saw a lot of people theorizing that, I thought it myself for a while too actually.