In order to understand the seven sacraments we have to realize that the early Church did not have the theology of sacraments that we have today – that is a development over time. In fact, the first time the seven sacraments that we have today were listed as such was in the 12th century with Peter Lombard’s classic work Sentences. However, in Scripture we see that some converts were baptized with water but “did not receive the Holy Spirit.” The then received what we today call confirmation (chrismation in the East).
Again, the seven sacraments we know about today were not the only “sacraments” of the early Church. However, they describe what Lombard eventually definined as the seven as being from Christ rather than from the Church. It’s just hard to find all the references because the theology did not yet exist to discuss them.
No, it would not be fair or correct to say that. What the Church did was an what Jesus did. That we don’t see Jesus marrying anyone doesn’t mean he didn’t institute the sacrament of marriage. In fact, in his discourse on marriage he established it as sacrament rather than the contractual understanding the Jews had. In baptizing he probably anointed with oil bringing the Holy Spirit in what we think of as Baptism and Confirmation/Chrismation. We know that Jesus healed the sick, and that is the sacrament of the anointing of the sick. Jesus certainly raised the 12 men he called to what would come to be called Holy Orders. And, of course, it’s clear that he celebrated the first eucharist.