No it wont frighten the finches but it can take a few weeks before they begin to use it. Where have you positioned it?
Rooks are not awful birds - they are Corvids and are amongst the most intelligent the same as crows and magpies. I can understand that their noise is off putting but does it help to think about what is going on in the rookery? Think of it like a big family home! They have all woken up and, firstly, they have all survived the night which is a cause for celebration. Then there is the day to day chat to get out of the way while they are preening themselves (like us having a shower) and tidying their nests and roosting places (like us doing our housework before going to work). Once this has been done then routes have to be worked out for the nearest and best food source. Although they will mostly all set off in the same direction they will normally land somewhere for a while and then peel off in different directions. They will all meet up again in the evening before setting off for their roost and then they natter all the way home. They are living out their lives much as we do - I expect the noise of our cars, lawnmowers, strimmers etc. gets on their nerves too! I often have to attend courses held in an old manor house. There is a well established rookery in the parkland close to house. This time of year it is lovely to watch the celebrations as a baby leaves the nest and takes its first flight. I often forget I am meant to be listening to the speaker!
They don't normally take nestlings but will eat ones that have died already.
As for doves we started off with one pair and now have up to twenty all the time.
Nature can appear cruel purplenanny but the sparrowhawk you saw taking birds from the feeder also has young to feed. It's just the way it goes. In feeding birds in our gardens we have increased the sparrowhawk population as we have set up fastfood restaurants for them and more of their chicks are surviving. I have a pair that live in the copse just over the road from me and they bring their young to practice flying from our roof to the garage roof opposite. I find it amazing that whenever they are around the whole garden freezes - not a movement from the small birds.
Have a look at the clever rook here
http://news.bbc.co.uk/1/hi/sci/tech/8059688.stmTaz x