1)
Why must he count seven days after becoming Tahor?
1.
Rashi (from Mo'ed Katan 15b): It means, after separating from the Mes [he needs seven days to become Tahor via Mei Chatas].
2.
Radak: Perhaps this will be an additional Kedushah in the future ? after Taharah at the end of seven days, he will count another seven days [Malbim ? before entering the Mikdash].
2)
Why does it say "Yesaperu Lo"? It should say Yispor Lo!
1.
Radak (27): His brethren the Kohanim count. If he forgot, they do not let him enter until he becomes Tahor after seven days.