Did the presbyterian church influence the formation of government for the US?

Yes - Presbyterians from Scotland were a significant group in the early colonies and they organized the church along Presbyterians lines, of course. One of the concepts that they employed in structuring their church government was that the authority in the church is divided among the various groups. Thus, the pastors have certain rights and duties, the Session (made up of people elected from the congregation) have others, and the local Presbytery (a group of Presbyterian churches in an geographical area) has yet another sets of rights and duties. For example, the Session alone determines the church budget, while the pastors are the ones who decide who should be baptized. However, the local Presbytery actually owns the church's property.

This all sounds boring perhaps, as it is the old separation of powers in the Federal government as we learned in school. But the Presbyterians had the idea first and the US founders adopted it.