My friend you have all of my sympathy for the lemon you've got. You should stay with your good old (D7) 406, you have had before, or at least buy the new (D9-D10)Peugeot 406. It never lets you down in disapointment. It is also much elegant and roomy and if we talk about reliability, this brand name is well known for ever lasting cars.
What you are describing is actually a pretty good example. All 156 have a fuel gauge that is innacurate as it gets below the 1/4 full point - it takes a few minutes to settle down. The back brake squeal is something that a lot of people experienced and is fixed very quickly by the dealer. Enjoy the car for what it was designed for - it's engine, handling and elegance.
UPDATE FROM OWNER - Now 2 and a half years and 33k miles into ownership - what can I say? 156 continues to be great to drive and attracts stares like no other car I've ever had. But the irritating problems persist - a permanently leaking sunroof, snapped exhaust hanger, leaking gearbox, unpredictable air-con, suspect clutch master cylinder. Having said that, I have never been left stranded, but annoying nonetheless. My conclusion is that you have a choice - reliability issues with the trade off of fantastic looks, styling and driving experience (ie Alfa), or reliability and a more mundane form of transport (other manufacturers!). Residual values continue to be a cause of concern - I've been offered £6k for a car which had a list price of almost £20k less than three years ago - so it looks as though it is going to be a long term relationship!
I can agree with the above comments. I was about to try to get my fuel guage looked at, maybe I shouldn't worry. I was also interested to read about the front tyres; Milcars sold me a second hand model with the canvas exposed on the inner edges. Doesn't say much for their 'pre-delivery inspection', does it? Love the car now it's re-shod. Getting just over 30mpg, which is a good return for the fun it gives.