The answer to your first question is not as clear in Canon Law but the answer to your question seems clear to me.
The canon you are referring to is Canon 428 which says that no innovations can happen during the time of the Diocesan Administrator; however how the Church interprets this question varies.
For example, the previous canon, Canon 427, seems to define this by saying the Diocesan Administrator cannot do anything prohibited to him by the law.
There are some factors that are unknown from your original question which would be needed for an accurate answer.
- Is he really a Diocesan Administrator or is he an Apostolic Administrator?
(The first is identified by the College of Consultors and the second is named by the Pope.)
From what you say, I will assume he is a Diocesan Administrator but just in case he is an Apostolic Administrator know that the Apostolic Administrator has all the powers of the Diocesan Bishop.
- How are you defining Financial Administrator?
That is not a canonical term.
- Is he literally the Diocesan Finance Officer, is he the Chancellor?
- If he is the Finance Officer, then what happened to the old one?
- Did he resign or was he fired?
If he resigned legitimately, the Diocesan Administrator could appoint a new one after consulting the College of Consultors.
- Is changing the way finances are done by requiring two signatures an innovation such that it would be illegal?
That depends on what was happening before. If there was a real problem such that the new Finance Officer was alarmed and the Diocesan Administrator consulted with the College of Consultors and it was clear that a problem needed to be fixed — I do not see that as an innovation.
As to your second question, the Finance Officer clearly has the right to audit parishes without any indication of wrongdoing. Backing this up by canons is complex but start at Canon 1278.
From your question it sounds to me like the Diocesan Administrator has inherited some problems and he is trying to see how widespread it is.
Hopefully you will get a new Bishop soon who will restore some stability to your diocese.