Gemara

(Ula): If Yisrael were half Tehorim and half Temei'im, we send one of the Tehorim to Derech Rechokah.

He did not say to be Metamei him through a Mes, for then he could not bring Chagigah;

Ula holds that the last six days one may bring Chagigah are compensation for the first day. Only one who could have brought it on the first day may bring it later.

93a (Beraisa - Rebbi): If a Nochri converted or a minor matured between Pesach Rishon and Sheni, he must bring Pesach Sheni/

R. Noson says, only one obligated to bring Pesach Rishon is commanded about Pesach Sheni.

Rebbi holds that Pesach Sheni is an independent obligation, even for one who was not commanded about Pesach Rishon;

R. Noson holds that it is compensation for the Rishon

Rishonim

Rosh (10:41): Bahag says that if one omitted Sefiras ha'Omer one day, he does not count afterwards, for we require "Temimos" (seven full weeks). The Ri disagrees. Every night is a Mitzvah by itself.

Tosfos (Menachos 66a DH Zecher): Bahag's opinion is astounding. It cannot be correct.

Poskim

Shulchan Aruch (OC 489:8): If one forgot to count a day, he counts the remaining days without a Berachah.

Kesav Sofer (OC 99): Seemingly, if one became Bar Mitzvah or converted during the Omer, even if he did not count beforehand he may count with a Berachah. He was exempt until now. Counting every day that he is obligated is "Temimos". R. Eliezer requires a Sukah proper for all seven days. He agrees that if one converted or became Bar Mitzvah during Chol ha'Mo'ed, he makes a Sukah, for until now he was exempt. However, he learned from a verse. Without a verse, it is not considered a Sukah for the entire Chag, even though he was exempt until now. Even if R. Eliezer learns from there to the Omer, Chachamim have no source. However, if he counted until now, even though it was Reshus (optional), it joins to be called Temimos. The same applies to one who counted without intent [according to the opinion that Mitzvos require intent], or intended not for the Mitzvah. The Noda b'Yehudah (1 OC 27) says that if an Onen was forbidden to do the Mitzvah, he may not bless afterwards, for this is not Temimos. However, what a child counted was a Mitzvah of Chinuch. Perhaps we hold like Tosfos, that due to Chinuch he is like one who was obligated. This is like one who is unsure if he missed a day; he counts with a Berachah.

Birkei Yosef (20): If a minor became Bar Mitzvah during the Omer, or someone converted during the Omer, or if one was an Onen for an entire night and day and the burial was not until Tzeis ha'Kochavim, afterwards all of these count without a Berachah (Mizrachi, in Pri ha'Aretz 3:7).

Sha'arei Teshuvah (20) and Kaf ha'Chayim (94): This law of a minor who became Bar Mitzvah does not apply to us, since our minors count from the age of Chinuch, especially a Mufla Samuch l'Ish (in the year before maturity). If he did not count until he matured, and some days of the Omer already passed, surely he may not bless.

Yabi'a Omer (3 OC 28): Why does he say 'us, since our minors count...'? All agree that one must train a child who knows how to count! This is the custom everywhere. If Pri ha'Aretz discussed one who did not count before maturing, he should have specified! Also, it was obvious to Sha'arei Teshuvah that in such a case he counts without a Berachah. Why did Pri ha'Aretz need to learn [from Chagigah,] from a lame person who became healthy on the second day? Rather, he discusses one who counted before maturing. What a minor counts does not exempt himself for after maturity. Machazik Berachah understood that Pri ha'Aretz holds that even if one counted on the day he was an Onen, he was exempt, so afterwards he cannot count with a Berachah. A minor is similar. The only case Pri ha'Aretz found in which he blesses after maturing is if he matured on the first day. Also Maharash Angil brings so from Chidushei ha'Rim. Nehar Shalom says that exemption from counting [of an Onen] is like forgetting to count. Either way, this is not Temimos. We may learn from there to a minor.

Yabi'a Omer: I question Pri ha'Aretz' proof from Chagigah. There, he was totally exempt while he was lame. A minor was obligated mid'Rabanan! Perhaps he holds that a [Mitzvah] mid'Rabanan cannot exempt a Torah [Chiyuv], or that a Mitzvah that is mid'Rabanan for two reasons (if Sefiras ha'Omer nowadays is mid'Rabanan even for adults - PF) cannot exempt a single mid'Rabanan. However, Hagahos Maimoniyos (Hilchos Evel 4:5, citing Semak) said "some say that an Avel on Motza'ei Shabbos does not say Havdalah after burial on Sunday. One can distinguish Torah Mitzvos from mid'Rabanan Mitzvos." However, perhaps Sefiras ha'Omer nowadays, which commemorates the Mitzvah at the time of the Mikdash, is unlike a proper Mitzvah mid'Rabanan such as Havdalah. I saw that Har Tzvi (OC 2:76) holds unlike me. I wrote what seems to me.

Aruch ha'Shulchan (15): One who became Bar Mitzvah continues to count with a Berachah only if he counted until now with a Berachah.

Question: If one forgot to count the Omer one day, he need not count at all afterwards, for we require "Temimos"! According to R. Eliezer, one who did not dwell in a Sukah on the first day does not build a Sukah during Chol ha'Mo'ed, for he cannot fulfill "ba'Sukos Teshvu Shiv'as Yamim"!

Answer (Mishpetei Uzi'el OC 22): Sefiras ha'Omer is different. If he does not count all seven weeks, he does not fulfill the Mitzvah. The same applies to Sukah according to R. Eliezer. He learns from "ha'Ezrach" that if one converted or matured during Sukos, he builds a Sukah. Why are they better than an adult Yisrael? The verse shows that the Torah was particular about a Yisrael who had a Chiyuv to be in a Sukah. The minor or convert were commanded only from when they matured or converted. The same applies to all Mitzvos that continue over time. They take effect on each person from when he became obligated to observe Mitzvos, even if he was exempt when the Mitzvah started.

Har Tzvi (OC 2 76): Seemingly, we learn from Yevamos 62a. R. Yochanan and Reish Lakish argue about a Nochri who had children and then converted. R. Yochanan holds that he fulfilled Peru u'Rvu through his children when he was exempt. The Turei Even asked that one is not Yotzei through Matzah he ate while exempt (Rosh Hashanah 28a)! The Minchas Chinuch (306) and Pri Yitzchak (R. Yitzchak Blazer) answered that Peru u'Rvu depends on having children. Taking a wife is merely Hechsher Mitzvah. This is difficult. Tosfos (Gitin 40a DH Lisa) says that the Mitzvah is fulfilled through a full Bi'ah, i.e. even before children! One cannot learn from Peru u'Rvu to Sefiras ha'Omer. However, presumably if a minor counted the Omer and matured, what he counted obligates him to finish counting after maturity. It did not exempt him of his current Chiyuv. Now, he counts and blesses every day! Rather, the Rishonim who hold that if one missed a day, the Mitzvah is Batel, do not say so here. He counted when he was a minor. He did not miss a day!

Avnei Nezer (539): If one did a Mitzvah when he was insane, he was not Yotzei (Rosh Hashanah 28a), for he was exempt at the time (Rambam Hilchos Chametz 6:3). Likewise, what a minor counted was not a Mitzvah. Poskim argue about whether one who missed days may count the rest with a Berachah. The Turei Even says that a lunatic was not Yotzei because it is as if he was Misasek. If a minor said the number of days, this shows that he intends for the action of counting. However, we hold that Mitzvos require intent, and there is no proof that he intends for the Mitzvah.