Saw the movie on Monday. These points may have been addressed here and I missed it, but just in case, this is dealt with to some degree in the movie(s); we can reasonably infer that Venom knows who Spider-Man is because he shares the knowledge of other Venom symbiotes throughout the multiverse (presumably including the Venom from Spider-Man 3) as per the Venom end credit scene. Eddie was transported along with Venom because they essentially share a body.
Electro doesn't directly state how he knew that Peter Parker is Spider-Man, but he does make a point to say that he was tapped into the computer system, assimilating data, when he was about to die which is one possible point (learning his identity through stored security footage or extrapolating it himself from multiple data sources, etc.) I wouldn't read too much into his statement that he thought Spider-Man would be black; this happens after he's been de-powered and is having his first real conversation with Andrew's Spider-Man since ASM2; he could easily have meant that he thought Spider-Man was black for most of ASM2 before finding out his identity, and this is the first opportunity he's chosen to bring it up.
Electo's different appearance in this film is given a lot of commentary to confirm that he's the same version of Electro from ASM2; he basically has the power to make himself look however he wants because of the different energy in the MCU. (There's a funny exchange between the Lizard and Electro about his "makeover".)
The ending of ASM had Conners with a few patches of scales; it's entirely possible that he wasn't completely cured by the end of that film, potentially explaining his appearance here and the different "look" of Andrew's cure. (Certainly the comic version reverted to his lizard form many times over.) I don't think there's any firm indication about when he or Sandman were plucked from their universes; it seems reasonable that they might be from the "present day" of their respective universes like Andrew and Tobey's Spider-Men.
(The believability or lack thereof of Strange's spell seems to be controversial here, but I'd speculate that the spell is drawing people in from the "present day" if they're still alive or if they're dead, from a sort of cosmic "save point" right before they die in order to fulfill the corrupted objective of "bring everyone who knows Peter Parker is Spider-Man to the MCU". This ups the stakes since Strange isn't just holding back everyone who knows Peter's identity in the whole multiverse, he's holding back everyone who ever knew his identity, the living and the dead. Dunno if this works with Venom or not; depends if there's a time jump between Venom 2 and the scenes in Mexico. Might hold up if Venom 3 doesn't come out till 2024.)
It is sort of convenient that the main people who slip through before Strange traps the spell are the villains and Spider-Men from the five previous Spider-Man films, but we can assume from Venom's appearance that there may have been others out there who didn't happen to be in New York or chose not to seek Peter out.
Regarding the Statue of Liberty, I believe it's shown to have been repaired by the end of the movie, so Elena could be referring either to the "improved" version with the shield or implying that the "new" [recent] removal of the planned shield improved the statue depending on the placement of the scene; that probably works either way.
The movie doesn't particularly hinge on all of the villains returning to their certain deaths, I don't think, it's just true for enough of them (Doc Ock, Goblin, and Electro) that Peter wants to prevent them from being returned. (In addition to wanting to cure all of them generally.)
I'll probably see the movie again; there may have been things that I missed or misinterpreted. Pretty cool way to start bringing in the other films as different parts of the multiverse. (Loved seeing Daredevil too.)