G'day mate, I have a '00 156 TS 5SP Manual and have found it to be a trouble free purchase. To answer your questions:
1. I can't really speak for the selespeed but my manual has been very economical fuel consumption wise, about 7-8L/100km in the city (mind you I don't see much peak hour). Official figures in AUS (govt tested) are 9.5/5.8L/100km.
2. I haven't really encountered many problems, although my car has low kay's (58,000!). I recommend you get the RACV or an Alfa mechanic (independant, not dealer) to check out any potential purchase. My main gripes are only really niggles such as the pathetic element antenna, which struggles to pick up AM. I had an extra AM antenna installed inside the front windscreen so I can listen to the footy/races. The aircon is really only barely serviceable for Australian conditions and you need to do a lot of fiddling to find the right combination of settings to make the cabin habitable in the summer. Poor turning circle is a bummer. Then again, these things are only a minor annoyance and really of no consequence to me in the bigger picture because I own one of the world's most beautifully designed motor cars. Sporty too, if driven with verve.
3. Can't say really what to look for but as I said earlier, get any potential purchase checked out by an expert.
4. Mine is in for service now at an Alfa dealer. It's having the equivalent of an 80,000km service which they estimated at $670 including parts. I was aware that the rear brake pads and disks were gone and sure enough they rang me and quoted an extra $400 for parts and labour. So not really cheap to service but about average for a european car in its class, probably cheaper that a Merc or Benz though I'm not sure. EDIT: I forgot to mention that it needs the timing belt changed every 50-60,000km so one with 98,000km's will be up for one soon. (In AUS they say 50,000km but in UK they say 36,000miles, which is 57,600km. I had mine done at 54,000km) I think that costs about a $1000-$1200, can't remember since I tried very hard to forget that service bill!
Finally, I would recommend you look for a manual. Selespeed does not really get the best out of the engine IMHO. Having said that, if selespeed appeals to you then you will probably get enjoyment out of it anyway, as many selespeed owners will attest. Just my two bob's worth. Either way, the 156 is a great buy.
Oh, and here's a good article
for you to read.