Some comments.
As swerve said, the limitations in the design of Navantia are mainly the derived of the commitment of capacities of an amphibious assault ship (a LHD on this case) with a secondary STOVL aviation role, against the aviaton capacity of a dedicate STOVL aircraft carrier without or with a minimal amphibious capacity.
About your second question, the answer is yes. The Navantia's SPS/BPE is capable of operating the F-35B and the AV-8B+ as well. This was one of the requests of the Spanish Navy during its design, given its interest on an alternative platform to PdA (R-11 Príncipe de Asturias) for sustained operations with Harrier and its future succesor. This was the main reason for the reject of the firsts designs of the Navantia's SPS/BPE that didn't have sky-jump neither were capable to operate with STOVL planes (with reasonable payloads) or the Osprey Tilt-Rotor. On it's max. air operation configuration the Navantia's ship have a capacity for ~35 STOVL aircrafts and helos.
Oh yes, yes. The Armaris Mistral, and Navantia's SPS/BPE both are less expensive than the LPD-17. The SPS will cost to Spanish Navy 360 mill € (~455 mill US$), the two smaller Mistrals for the French Navy cost to France around 600 mill € (~760 mill US$). But the ninth LPD-17 proyected cost (As said FY2006 budget) will be over 1,6 million US$.
Well, it would have to be many cuts and not only about the titanium, to cut more than 500 mill $ (almost 1/3 of the LPD-17 cost), in each ship, so comply with the budgetary limit of the Australian program would be very complicated. A lot more if we keep in mind the investment and cost of a foreseeable local construction of equipment and/or part/totality of the ships. We don't forget that the contenders are not the European shipyards by their own, but teams of Australian and European shipyards: Navantia-Tenix and Armaris-ADI.
IMO, if Australia decides to acquire an helo for AEW tasks, the logical thing will be opt for an AEW variant the NH-90, already planed to be developed for the Spanish Navy. Introduce a new logistic chain for the Merlin only for a few AEW helos??? With the recenly purchase of the MRH-90s, I don't think so.