How could Fëanor have hoped to defeat Morgoth?
Even though Fingolfin managed to hurt Morgoth, he basically had no chance. Also he was just fighting Morgoth in a duel, while Fëanor would have had to kill all kinds of enemies before even reaching Morgoth.
Manwë makes this same point to Fëanor, actually, so we get to hear his response (emphasis mine):
But even as the trumpet sang and Fëanor issued from the gates of Tirion a messenger came at last from Manwë, saying: 'Against the folly of Fëanor shall be set my counsel only. Go not forth! For the hour is evil, and your road leads to sorrow that ye do not foresee. No aid will the Valar lend you in this quest; but neither will they hinder you; for this ye shall know: as ye came hither freely, freely shall ye depart. But thou Fëanor Finwë's son, by thine oath art exiled. The lies of Melkor thou shalt unlearn in bitterness. Vala he is, thou saist. Then thou hast sworn in vain, for none of the Valar canst thou overcome now or ever within the halls of Eä, not though Eru whom thou namest had made thee thrice greater than thou art.'
[...]
Then turning to the herald he cried: 'Say this to Manwë Súlimo, High King of Arda: if Fëanor cannot overthrow Morgoth, at least he delays not to assail him, and sits not idle in grief. And it may be that Eru has set in me a fire greater than thou knowest. Such hurt at the least will I do to the Foe of the Valar that even the mighty in the Ring of Doom shall wonder to hear it. Yea, in the end they shall follow me. Farewell!'
The Silmarillion III Quenta Silmarillion Chapter 9: "Of the Flight of the Noldor"
Basically, Fëanor doesn't necessarily intend to defeat Morgoth; that would be a nice bonus, I'm sure, but Fëanor will settle for causing as much grief as he possibly can.
This isn't a terribly sensible response, but that fits; it's a mistake to seek rational motives for Fëanor's actions. We see time and again that his temper leads him to do things that are...unwise, to say the least. This is just another example of his hot-headedness getting him into trouble.
Fëanor embodied the fire aspect of the Noldor.
Fire, or an affinity with fire is used by Tolkien to denote construction, particularly the construction of artifacts, or modification of one's environment, metaphorically or otherwise.
Fire is also seen to represent rebellion, and indeed one only needs to look to the "Flight of the Noldor" to see how similar in thinking Morgoth and Fëanor are.
Fëanor, the Noldor, Morgoth, Sauron,Saruman and Gandalf all are linked with being facile with fire, as well as having the classical aspects associated with fire, quick to anger, emotionality, confrontation, and charisma. I would expect Fëanor to defeat Fingolfin in any kind of duel, and if any mortal creature could defeat a Vala, Fëanor would have been the one.
In fact, it can be defined as victory for a mortal creature to cause an immortal one eternal suffering. Fingolfin achieved this. Fëanor is a much more capable creature, and would be expected to be able to inflict more damage. He would have died doing this, but that certainly beats suffering for millennia from the aftereffects of the battle.
