First of all BT Plus can't change the laws of physics, if your speed was below the previous Infinity1 speed cap it won't change. Speed is related to the distance from the cabinet.
The speed of your line is optimised by a system called DLM (Dynamic Line Management) which employs a number of technologies to give you the maximum speed your line can support. When you upgraded to BT Plus, this sytem reset everything back to default including removing a retransmission technology (G.Inp). Once DLM has had a chance to analyse your line, it will re-instate G.Inp with a commensurate increase in speed.
this is not correct, you won't get double the discount - it will simply be referring to the discount you're recieving on BT Plus. Your package is £39.99, discounted from £58.99 - THAT is the discount that carries on, not your current discount. You will not and should not recieve 'double discount'.
It does in fact state further down in the even smaller small print that the freeze applies to line rental and broadband only. It does create some ambiguity though as the most prominent line is "We may change any prices....".
It could, and should be made clearer, it's not surprising that customers get told different things when contacting Customer Support. Proper beta testing and vetting would improve their communication markedly.