Jagal

Hi all, I am slightly new to Citroen. I bought a 4 year old C5 a few months ago. I noticed that the two back tyres are different brands to the two new front ones. One of them will need replacing in the next few months. I was reading about TPMI and when I press the button CHECK on my dash nothing comes up other than service due in XXXXX miles and NO Faults. The back tyres have a valve that has a corroded metal bit coming out of the allow wheel. The front ones look like normal black valves (rubber). If I could ask the collective advice on the following: 1. Am I right in saying my TPMS is deactivated? 2. Is TPMS something to stay well away from? (noted new legislation) Or should I reactivate it? 3. The tyres hold their pressure well - would you suggest changing both rear wheels? I have heard of tyres blowout with corrosion near the valve - I do a lot of motorway driving and would like to be safe.... Thanks!