The TO needs to serve a TPO on the tree subject of your current notice to prevent you taking the tree down. If he fails to do so within six weeks of your notice you may carry out the work as notified, you should have received an acknowledgement from your LPA to this effect. Your client will know when a TPO has been served on him! You can also check with the LPA.
Regarding the last chestnut, the TO should have done his job in the first instance, no point bleating about it now. However sounds like you may be dealing with the lesser spotted d*****d species of TO. He may decide to invite you in for a PACE interview. Make sure you have all records and correspondance in order. I wouldn't even attend just forward the documentary evidence with a factual covering letter. You know date notified, acknowledgement received on, no objections letter received on, tree felled on etc.
Sounds a bit like a TO I've had dealings with where are you based?
Dom