It is forbidden to use electricity on Yom Tov just as is the law on Shabbos.^[1]

May one raise the temperature of an electric oven or stove on Yom Tov?^[2]

No, unless one knows for certain that doing so will not extinguish any current currents and will not ignite any new currents of heat. However, some Poskim^[3] are stringent even in such a case.

May one use ovens freely on Yom Tov even if they are thermostat based without Shabbos mode?^[4]

Yes.^[5]

May one ask a gentile on Yom Tov to turn on the electricity/light?^[6]

It is permitted to ask a gentile to turn on a light on Yom Tov for the sake of a Mitzvah, or in a time of great need.^[7] It is forbidden to do so if it does not involve a Mitzvah or great need.

May one ask a child on Yom Tov to turn on the electricity?

Some Poskim^[8] rule that in a time of need one may ask a child that has not reached the age of Chinuch, to turn on the electricity for the sake of Simchas Yom Tov.

If one transgressed and turned on the electricity on Yom Tov may he benefit from it?

Yes, just as we rule regarding fire.

May one set up an electric oven to turn on, on Yom Tov, using a timer?^[9]

Yes. It is permitted to cook/bake in an electric oven that was turned on before Yom Tov or that was turned on using a timer.

[1] The reason: As it creates a new fire.

[2] Piskeiy Teshuvos 502:2; Nitei Gavriel 20:11

[3] Beir Moshe 8:139; Rav Yaakov Yosef says it adds a new current and is thus forbidden.

[4] SSH”K 1:30

[5] The reason: As even if one causes the fire to extinguish [by closing the oven door] or turn on [by opening the oven door] this is an indirect action, Grama, and by a Psik Reishei of Gram Kibuiy or Havara one may be lenient. [Rav SZ”A ibid footnote 80]

[6] Minchas Yitzchak 3:37; Or Letziyon 20:6; Yom Tov Kehilchaso 22:8

[7] The reason: As doing so is a Shevus Deshvus on Yom Tov, being electricity is forbidden due to igniting a flame, which is only Rabbinically forbidden on Yom Tov.

[8] Beir Moshe 8:166; Piskeiy Teshuvos 502:2

[9] Nitei Gavriel 9:16