I. When can you make Kiddush?
On Friday night the Gemara in Berachos states that a person can daven early as well as make Kiddush early (before nightfall). This is generally assumed to be because when you are mekabel shabbos early it turns day into Shabbos.
What about on Pesach night?
The Gemara in Pesachim comments based on a Pasuk that the Korban Pesach needs to be eaten at night. The Rishonim add on, that likewise the other mitzvos (Matzah and Maror) which need to be eaten with the Pesach need to be at night as well. The Shulchan Aruch adds on that you can't make Kiddush until night either. Why not? The Magen Avraham explains that Kiddush is the first of the 4 cups and just like the other Mitzvos need to be done at night , so too the 4 cups because כעין דאורייתא תקנו. The Taz ofers a cryptic suggestion. RYBS explained the Taz as follows. Kiddush is part of Magid, it is the beginning of the telling of the story of yetzias Mitzrayim and therefore as part of Sippur Yetzias Mitzrayim it needs to be at night.
II. Can you use grape juice?
There is a general dispute whether you can ever use grape juice for Kiddush, we will not get into that. Assuming that in general you can, what about Pesach night? The gemara in pesachim comments that if you drink יין חי, you are יוצא the 4 cups, but you are not יוצא חרות. What is יין חי? It is undiluted wine. The wine in the time of Chazal was basically undrinkable without diluting it.
Based on the fact that the gemara said that יין חי is not יוצא חרות a number of poskim say the same applies to grape juice. Since it is not alchoholic it is also not a sign of freedom. Others disagree and say that there is no comparison. יין חי is undrinkable wine, no one drinks it. Grape juice is drunk and enjoyed by many and therefore you would be יוצא חרות if you enjoy it.
Bottom line is if you can drink wine it is better to drink wine.
III. How much do you need to drink?
On Friday night you need to drink a cheekful of wine which is a a majority of a reviis. What about Pesach night? On Friday night, there is no chiyuv to drink wine per se, rather since you are making a beracha on a cup of wine you need to drink from it. On Pesach night there is a chiyuv not only to make kiddush but drink 4 cups of wine. Kiddush is one of those, and therefore you need to drink either the whole cup or at least a majority of the cup.