Can restricted funds or donations be taken if a parish is sued?
Generally no. This answer will be definitely no if the parish observes the corporate formalities of doing annual reports and preparing corporate minutes, and keeps its book of accounts in good order (including proper documentation of the restrictions imposed by the donors of the funds).
If a parish is sued and in the middle of a capital campaign such as building a new facility are those funds vulnerable in the suit?
Restricted funds will escape execution for the payment of parish debts, but in order for the funds raised for building or other restricted purposes, the collection of the funds will need to be well-documented to show that the funds are restricted. Once the funds' restrictions are well-documented, they will not be in jeopardy of being lost for general liability executions against other parish properties.
If a parish is sued is there a homestead law that would protect it from losing the church?
No. The homestead law in Arizona pertains only to single family residences.