Can I receive communion in an Anglican church?

No. The Anglican church does not have valid holy orders, therefore, eucharistic intercommunion is not possible.

Catechism states the following:
Ecclesial communities derived from the Reformation and separated from the Catholic Church "have not preserved the proper reality of the eucharistic mystery in its fullness, especially because of the absence of the sacrament of holy orders." It is for this reason that, for the Catholic Church, eucharistic intercommunion with these communities is not possible.

I go to a protestant school, more like a school that welcomes all Christians and not just protestants, and I participate in their worship services. Can I, a Catholic, receive the protestant communion?

No, the Church does not permit Catholics to receive communion in Churches not in union with the Catholic Church (canon 844 §1).

There are rare exceptions that can be made for Catholics who do not have access to a Catholic church or minister but this would only be for Churches that have a valid Eucharist (e.g. the Eastern Orthodox Churches). The Church does not permit intercommunion under any circumstances with Christian faith communities that do not have a valid Eucharist
(canon 844 §2).

Simply being at a Protestant liturgy does not meet the standard necessary for the exception to the prohibition of intercommunion.