1. Before the start of the Seder:

It is forbidden to eat or drink anything prior to Kadesh, just as is the law regarding Kiddush of every Shabbos and Yom Tov.[1]

Giving a child food to eat before Kadesh?[2] [In general it is forbidden to eat prior to Kiddush, and one may not delay the start of the Seder after nightfall, however,] if one is unable to begin the Seder [i.e. Kadesh] right away at the beginning of the night, and the children are hungry and desire to eat, then one may give them a small amount of food to eat [even prior to saying Kiddush]. [It goes without saying that one may give them a small amount to eat after the start of the Seder, as explained in Halacha 7. This applies to children of all ages, even above the age of Chinuch, so long as they are below Bar and Bas Mitzvah.[3]] However, one is not to allow [children who are above the age of Chinuch] to eat a lot of food, and he is thus to remove the plates from in front of them [once they have eaten a little amount], in order so they do not fall asleep during the recital of the Haggadah.[4] [However, children who are below the age of Chinuch[5], may be given even a large amount of food to eat.[6]]

Giving a child Matzah to eat before and during the Seder?[7] (It is possible that prior to saying the Haggadah, it is forbidden to feed children [who are above the age of Chinuch] Matzah which is Kosher for the night of the Seder [i.e. Lechem Oni], even in a small amount.[8]) However, children who are below the age of Chinuch[9], may be fed Matzah on Erev Pesach and prior to Haggadah.[10]

Summary: It is forbidden to eat or drink anything prior to Kadesh, just as is the law regarding Kiddush of every Shabbos and Yom Tov. Prior to finishing Maggid, one may not give children, who are above the age of Chinuch, Matzah to eat until the end of Maggid, although one may give them a small amount of other foods to eat even prior to the beginning the Seder.

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[1] See Admur 484:5; 271:9

[2] Admur 472:23; Rashbam Pesachim 109a

[3] See Admur 269:3; 343:7; 106:3; SSH”K 52:18; Piskeiy Teshuvos 343:1

[4] The reason: Although it is permitted to give children [even above the age of Chinuch] food to eat prior to hearing Kiddush and the Haggadah, as ruled in 269:3 and 471:10, nevertheless, one is to hasten to remove the food from in front of them, and not allow them to eat a lot in order so they do not fall asleep during the recital of Haggadah. [Admur ibid]

[5] This refers to a child who is not old enough to understand the story of the exodus that is told to him [on the Seder night]. [Admur 471:10]

[6] See Admur 471:10

[7] Admur 472:23, parentheses in original

[8] The reason: The reason is based on that which was explained in 471:10 [Admur ibid] that a child who is old enough to understand the story of the exodus that is told to him [on the Seder night], may not be fed Matzah throughout Erev Pesach. [Admur 471:10; Rama 471:2; Terumos Hadeshen 125] The reason for this is because once the child is old enough to understand the story of the Exodus there is a Mitzvah for his father to teach him the story as written in the Haggadah, and included in this story is the verse “For this sake [of us fulfilling the Mitzvah of eating Matzah and Maror-Rashi] did Hashem remove you from Egypt”. Now, if the child has already filled himself with Matzah how can he be told that it is for this sake, [as the Matzah is no longer a novelty for him-Machatziz Hashekel]. [Admur ibid; M”A 471:7; Terumos Hadeshen 125] Now, due to all this, possibly such a child may not eat even a little bit of Matzah, even after nightfall, prior to finishing the Haggadah. [Admur 472:23] Vetzaruch Iyun as to why this Halacha is in parentheses, and as to why Admur is in doubt as to its ruling, writing that it is only “possibly forbidden.” Perhaps, however, the reason is because once nightfall begins, the time of Maggid has arrived, and it is thus possible that there is no longer a contradiction between the child eating Matzha before the Haggadah. Vetzaruch Iyun.

[9] This refers to a child who is not old enough to understand the story of the exodus that is told to him [on the Seder night]. [Admur 471:10]

[10] Admur 471:10 that a child who is not old enough to understand the story of the exodus that is told to him [on the Seder night], may be fed Matzah throughout Erev Pesach, as well as on Pesach even prior to Kiddush, if needed; Admur here references to his ruling there in 471:10 for the reason why one may not give children Matzah. Accordingly, one must conclude that the wording of “Tinokos” in Admur ibid refers to children above Chinuch and not to all children, otherwise it would directly contradict his ruling in 471:10!