Not specifically Airbus, but for #1...
No manufacturer entirely 'protects' the leading edge of the wing against ice; even those aircraft you might think of as having 'full span anti-ice' don't really - there's inevitably a little section at root and tip that is left to fend for itself.
The reason is that anti-ice protection 'costs' - both in terms of weight, and in terms of lost thrust (due to either bleed air or extracted power, depending on the AI system) - and the more wing you protect, the more it 'costs'. So it's in the OEM's interest to provide the minimal AI coverage for safety and certifiable operation.
The reason that generally the outboard is preferentially protected is that often it is the most critical area. Ice accumulates faster on small, sharp, objects than on the fat, blunt ones. (Hence the use of e.g. windscreen wipers as visual detectors, and the design of a typical ice probe - being small and sharp, they collect ice faster than the critical aerodynamic surfaces, and so give a useful warning). The outboard wing is inevitably smaller and thinner, hence ice accumulates there faster. So, for a given 'encounter' you'll get more ice outboard, so there's more value in protecting the outboard section.
Additionally, if the aircraft is going to retain certifiable stall behaviour when iced up, it's important that the outboard wing retain, as much as possible, it's nominal, clean, behaviour - a premature outboard stall, on a swept wing, will induce a pitch-up into the stall, generally considered uncertifiable. If the inboard stalls prematurely, although you may lose lift, you won't have an uncertifiable characteristic. So if you can afford the hit in stall SPEED, then the characteristics will be ok, so you leave the IB section to fend for itself.
There are of course exceptions. It might be that the critical section of the wing isn't outboard. It might be you can't afford any stall speed degradation and have to potection most of the wing. But that's the kind of reasoning that leads to a partially protected wing.
(And similar logic explains why LE devices, like slats, are also not always applied to the whole wing. Its a cost-benefit trade-off)
For #2. SAT is also important in considering icing accumulation - you may not have perfect recovery to TAT at the locations where the ice is accumulating, plus if the SAT is below 0 its far easier to have potential icing (supercooled liquid suspended in the air). Since TAT-SAT is a function of airspeed, the 10TAT is chosen such that even at the fastest speed considered, you'll still be above 0 SAT if you stay above 10 TAT. Below 10 TAT, at high speed you may be at, or close to 0 SAT.