No. The skirting and dado/capping are normally applied on top of the wainscotting. Try to leave a small air gap beneath the cladding at the bottom, say 1 to 1-1/2in (this is to prevent the panel "wicking-up" moisture in the event of a flood). The skirting will cover this. Either way lay out your horizontal line with a level and string line at the top of the wainscotting and work to that, not the other way round (floors aren't always level. Most of the wainscotting I've dealt with in pub and restaurant fit-outs (domestics, too) require horizontal battens (2 x 1in slate laths) fixed to the walls near the bottom and at the top of the wainscotting to which the wainscotting is then fixed. The battens are fixed with a combination of GripFill (NoNails) and masonry fixings (7mm hole, brown plug, #10 x 3in or 5.0 x 75mm CSK HD screws). The battens can be packed off the wall as required to make a straighter line, which looks better and makes neat joints achieveable. This will require a string line, a couple of MDF packers and a "traveller" (basically another piece of MDF) together with some thin plywood/plastic packers - if not sure ask). The wanscotting is then fixed to the battens using a pinner (16 gauge). The skirtings are similarly fixed using a 16 gauge pinner and dabs of GripFill, as is the dado/capping (which should be the type that overhangs the wainscotting a small way like a miniature window board rather than the type designed to plant onto the wall). If there is a slight discrepancy in the level of the top this can be covered by the use of a small cavetto moulding on the underside to cover that gap. Because you are in a bathroom it is imperative that everything is sealed well (back and front) and thoroughly sealed/painted after installation. I'd also recommend running a bead of silicone along the joints between the skirting and the floor as well as between the dado/capping and the wall. MDF, where used, must be MR-MDF (moisture-resistant, normally green)
If you do decide to go straight onto the wall, the cladding still needs to go on first, levelled to the top, and the skirting and dado/capping is applied afterwards. This only works if your walls are straight and flat. In this case the cladding is fixed to the wall using GripFill and 16 gauge pins
Out of preference I tend to prefer the yellow (non-solvent) GripFill for this sort of task - skins less, easier to clean up and can be used for wood to wood jointing
Also, if the flooring is out a bit, do I adjust the skirting to compensate so that the dado is level?
As stated above set your "waist" level and work
down from that. If needs be when the skirting is installed it may need to be scribed to the floor. The dado/capping may also need to be scribed to the wall if it is really bad
