PIP conundrum

Hi, I had my PIP reassessed last year and was given 0 points and all money stopped. Mandatory reconsideration was also 0 points. Put in for appeal which would take 57 weeks, my advisor told me to make a new claim which I did. Out of the blue I had a phone call from the PIP people saying they had looked at my 'new evidence' and would reinstate the 8 + 8 for mobility award for 5 years. Despite my saying I could not discuss anything on the phone he plowed on making me a mouthwatering offer. The way he spoke it sounded like he would give me the same points back and he pointed out that I wouldn't have to go to appeal. However, when I received their letter I have been given points for items I had not ticked and clarified, neither in the old assessment or the new application and the backdated payment sent to my bank. He also told me he had disposed of my new PIP application and the letter states that their previous decision regarding the other descriptors would stay in place. I don't like having points given to me which are not based on my written account (despite the fact they are true but not as pressing as all the others) and somewhat feel very uneasy about all of this. How would I go about challenging their choice of descriptors. Their letter makes no mention of a Mandatory Reconsideration and only states that I can appeal at a tribunal. Do I have to go for another Mandatory Reconsideration based on this new award first or can I go straight to Tribunal? Because my health has deteriorated considerably I would would prefer my new application to be considered, would it be possible to have all descriptors be considered by the judges or can they only look at the ones currently awarded? Any insight into this would be much appreciated. With many thanks!