1. How did Harry break into a maximum security facility all by himself? Or take out two trained guards by his little frail self. Isn't he supposed to be sick?
They let him in past most of the checkpoints because he was Harry Osborn, and OsCorp obviously had a lot of dealings with Ravencroft. And the sickness hadn't begun to really weaken him as badly as it did Norman (that took years).
2. Electro had the combined electric power of an entire city as his disposal. Why didn't he just instantly fry Spider-man, game over?
You have to be totally grounded for electricity to really hurt you. Spidey is swinging around in the air a lot of the time.
3. Richard Parker ran so they couldn't get his blood? Besides that making no sense, why did Mary Parker run too? Why didn't Norman Osborn just kidnap Peter and force him to come out hiding?
No one knew about Richard altering the Spiders so it would only work with his DNA. Him running was so no one would ever know. Instead of assuming he did something to the Spiders, they thought he was running with their research so they sent someone to kill him instead.
4. Where did Electro's black suit come from? Where does it go when he dissipates?
One of the guys experimenting on him at the Asylum was wearing it, probably some insulation suit to keep Electro from killing him. Presumably, there was a deleted scene of Electro getting it from the guy.
5. Harry's dad started getting sick at Harry's age. So Harry had 20 plus years to go. Why was he in such a hurry? Why was his first impulse to inject Spider-man's blood into himself or all things? Why not do, I dunno, an hour of research first? Hell, why didn't Spider-man suggest this option? to Harry?
Harry was just terrified at the sudden realization he'd be dead long before his time (60 ain't old anymore) and wanted a cure NOW. Norman told him that the Spider-Venom would heal him, and Harry was smart enough to realize Spider-Man was the successful result of the Human/Spider DNA thing so he figured an infusion of his successfully melded DNA would be enough.
Peter assumed that the blood would just mutate Harry like it did to Connors (who would also have done tests) and figured it was just unworkable. He's probably right, it would have turned Harry into Venom instead of the Goblin.
6. If the Goblin suit cured Harry so easily, why all the run-around with spiders and blood and other crap?
It was a combination of the venom and the suit that helped Harry. And it just replaced one disease with another. Now he uncontrollably mutates into a Goblin creature.