I'm using steel SIPS, but the discussion could include any kind of SIP skins.

What is the best way to apply tile to a steel SIP panel? I was considering using it in an exterior application, probably travertine or marble, but perhaps ceramic or porcelain. I suppose there is the paper backed lath and scratch coat substrate, but I wonder if maybe Durock might be better?

First apply diamond mesh with sheet metal screws, the proceed as required by your material of choice supplies/manufacturer.

For tile I think the 'Durock' (Fiberglass Mesh Reinforced Cement Board) is a good way to go. You need to put up a layer of at least 15# building felt first and then attach the cement board with corrosion resistant screws. The building felt serves two purposes, 1. it keep the cement board away from the SIPs to prevent corrosion and 2. it acts as a 'slip-sheet' to allow the two different materials (cement board and sheet metal) to move somewhat independently during thermal expansion and contractions of the metal SIPs. You have to tape and mud the joints of the cement board to unify the sheets too. Then you need to pick an exterior grade tile adhesive/mortar/grout that is flexible to attach the tiles. You must leave at least a 1/16" gap between tiles to allow for the expansion. If you have large uninterupted expanses of tile, you may need control joints periodically.

As a disclaimer, I happen to know the climate/region you are building in, so what I described above will work, but in other climates furring strips may be required between the SIPS and the cement board. The key is to understand how each material expands and contracts in relation to each other in the climate that you are building. Large temperature differentials can wreak havoc on building materials if you don't allow them to move when they want to move.

On a similar note, do you think building felt would be necessary before applying Hardieboard or Hardishingles (or similar fiber cement boards or shingles)?

Since I happen to know your home design and its climate conditions, I strongly recommend you use building felt under any cement board that you use for a siding application. The reason why is your design has very short roof overhangs, 2 story walls with parapet end walls and you live in a humid climate with a rainy season. Your walls are going to get wet and possibly saturated with water and you need the felt to separate the damp cement board from your metal SIPs to prevent corrosion.

However, I built a metal SIPs home for myself in Florida. I used 'Hardiplank' lap siding and applied it directly to the metal SIPs without using building felt, but my house has 3 foot overhangs and my walls are 1 story high. On most rainy days water never touches my walls because of the large overhangs, except for the occasional wind storm. In this specific case I think not using felt would be ok because I'm relying on the water shedding properties of the painted lap siding and the galvanized polyester painted metal skins of the SIPs to handle the occasional dampness I would get from a storm.

It's best to error on the side of caution with things like this and use the felt. It's not expensive, which makes it cheap insurance.

A paper backed lath and scratch coat will work, if you use durock you will still need a felt barrier.
Durock and tlle grout are both porous and will allow water thru, a felt barrier will prevent water intrusion and shed water away