I am currently planning a similar re-flooring job for my small bathroom that has a peel-n-stick vinyl tile floor. I've had many of the same questions as you; here's what I've found out (I'm no expert, though):
- LVP to my understanding has a grout-like central layer and thus needs to be well-supported to prevent cracking. My vinyl floor tiles apparently qualify as OK, so I will be installing on top of the existing floor. My manufacturer says a tile floor is OK too as long as its general subfloor smoothness conditions are met.
Approved subfloors: Concrete, Plywood, OSB, Particleboard, Chipboard, Hardwood (Solid,
Engineered, Parquet), Tile (Ceramic, Terrazzo, Stone, Asbestos, Peel and
Stick), Non-Cushion Sheet Vinyl, Metal, VCT, DRIcore
Must be level to within 3⁄16" in a 10ft. (4.76mm in a 3m) span; no
bumps or low spots.
Your sample seems to have a cork-like preattached underlayment. I would be concerned about using that in a potentially wet environment like a bathroom, where water may get underneath, be trapped and lead to rot. The product I am using is described as waterproof (i.e. no organic surface like cork and does not absorb substantial water), has a synthetic preattached underlayment and explicitly recommended for kitchens and bathrooms.
The LVP I am using is click-lock style, which IS a floating floor, and does not use any fasteners to hold the planks together or to the underlying surface. As the scalloped tongue/groove shows, it's designed not to be able to separate sideways once you angle in the next plank and rotate that down flat.
Because of the floating floor aspect, to account for expansion/contraction, my LVP maker recommends a 1/4-3/8 inch expansion gap around all sides. Baseboard or quarter-round wall/cabinet bottom molding, and surface transitions like door openings are not attached to the floor and will cover that gap. Toilets and tubs need to have the gap caulked with something that is very flexible and does not harden over time. In addition to the 100% silicone mentioned below, there are some specialty extreme flex caulking products available.
[it is] a floating floor and should be allowed to expand and
contract freely. It must not be glued, nailed, or fastened to the subfloor in
any way. Permanent cabinets, vanities, islands and similar items should
be installed first. Then, install the product around them, leaving the proper
1/4-3/8 inch expansion gap. The product can be installed under vanities with legs.
The product can be installed under toilets; leave proper expansion space
around flange and use a premium waterproof 100% silicone caulk. Do
not anchor toilet through the material.
- The toilet: There are two ways of dealing with this. One way is to remove the toilet, install the flooring right up to the flange (with expansion space and caulk), then reinstall the toilet with some kind of flange spacer or extra wax ring added to account for the raised height. The other way is to leave the toilet in place and install the flooring right up to the outside of the toilet (with expansion space and caulk, maybe no caulk in back so you can see any leaks). I haven't yet decided which to do, as I will also be installing a new toilet.
Edit: FreeMan makes an excellent point about the install around toilet:
The only drawback to laying the tile to the toilet (and not underneath) is if the toilet should ever need to be replaced the floor might have to be replaced as well because the new base might be smaller than the old base.
For similar repair/modify situations down the road, it's worth holding on to any extra LVP planks just as you would hold on to extra ceramic tiles from an install.