1. Looks like rubbish. Plenty of decent ones for the mk5 for a tad more, Kenwood, Alpine and I even saw a Zenec NC2010 for £350 on ebay the other day.
2. Yes I would ditch those tyres if you love your wife. I had a 7mm Conti SC3 go all cracked on the sidewall so had to bin it, anywhere that has these now is old stock. I got 225/40/18 Goodyear Eagle F1's for £93 each from lovetyres.co.uk, happy with them so far.
3. TPMS is odd, it works after about 10 miles of recognising an issue, it is a passive system. Best to manually check.
What you need to do is with the ignition on, hold down the TPMS button until it beeps, then it 'recalibrates' its knowledge