"...Does anybody know if under FOI or EIR a Parish Council is obliged to share details of the application they make to request a TPO..."
Yes they are - EIR is the correct path.
"...In my bites that are making the application because I asked for some pruning works which after 12 months of waiting for a solicitor to say if they own the land in which it sits, they said no works but they are going for a TPO...."
I can make no sense of this? What are your bites?
Are you saying there is a tree which is not yet subject to a TPO, you are not the owner of the tree, but you have asked the PC to prune it because it encroaches across your boundary but they question ownership of the land upon which the tree stands?
Could you be a bit clearer on the situation please?
If the PC requests a TPO it will be submitted to the Local Planning Authority for assessment (probably under the TEMPO system of tree evaluation.)
EIR would allow you to seek the PC submission to the LPA requesting the TPO and then you can EIR the LPA (some will publish TPO applications the same as any planning application) but some don't. In any case, if the LPA receives a request for a TPO, and if they decide to proceed through the qualifying process, every 'interested party' must be informed of the process.
Happy to provide much more specific detail if you could clarify the situation