It's celeste, looks like it has the made in Italy decal on the bottom of the seat tube and based on the color of the tubing decals one of the mid-to late 1980s models with Bianchi Speical or Formula II tubesets.

There were distinct flavors during this era. The earlier, circa 1985/1986 models were tyicially all Italian equipped often with Campagnolo Nuovo Record rear derailleurs, Modolo brakes and Ofmega or Gipiemme and sometimes Campagnolo Gran Sport parts for the remaining components. Circa 1987, they started to spec Japanese indexed derailleurs, typically SunTour Alpha 5000 or Cyclone 7000. The early all Italian bicycles seem to be more desirable and fetch higher prices, though they are not necessarliy better. Buyers also pay a premium for the celeste color. depending on the exact year, the original price could be anywhere between $550-$800 US.

My guess, based on the decals is that it is a circa 1988 model, probably with the SunTour derailleurs. What you need to do is go back to seller and ask specifically if it has a made in Italy decal, what the tubing decal says and what the make and models are for the major components (derailleurs, cranksets, brakes, hubs and rims. Knowing the serial number would help too. At that point the forum memebrs can advise you better. The only problem with these later models is that the SunTour indexing is not compatitble with other makes and replacements can be hard to track down.

Flats are not a typically big problem. New tubes are cheap. It sounds like a slow leak. Maybe he pinched it when he put the new tires on.

Regardless of the merits of the bicycle, the first priority is to ensure that it is the correct size for yourself and you are comfortable on it. To do that, you will have to ride it, unless you know your size from previous experience. Maybe the seller has an indoor trainer that you can use to test it?