First, let's answer the first to questions together, as they are closely related.
Does one lean with the bike?
Does the bike stay more upright?
Short answers are yes and yes in most cases.
To elaborate, let's take a look at what you're trying to achieve when cornering. I found this image recently and I think it does a great job of visualizing the basic physics of what's happening when you take a corner on a bike:
In a turn, whether you're leaning the bike, or your body, or both, that "local gravity" line is what's keeping you from highsiding or lowsiding. The center of gravity and that center line just moves depending on what you're leaning and how low you're getting.
Do a search for mountain bike cornering and a search for road bike cornering. Notice how centered the road riders are compared to the mountain bikers.
One of the big reasons for the "lean the bike" advice is to engage the more aggressive side knobs on a mountain bike tire. On a road bike this is not necessary.
With a mountain bike you spend a lot of time skirting the line of traction. You lose it and regain it often. Many of the techniques for cornering on a mountain bike are to keep you on the traction side of that line and to recover without crashing when you cross it. Many of these techniques aren't applicable on a road bike, where in most cases you either have traction or you've just crashed.
You'll also notice on the mountain bike cornering images that in big berms the riders are typically more centered over the bike, sharing the posture of the cornering roadies. That's because when traction isn't an issue being centered over the bike is the most balanced and stable way through a turn, and that's why you see road riders using that posture most of the time.
Is the pressure more evenly spaced among both pedals?
No. The advice on weighting of the pedals and the bars stays the same. Drop the outside pedal and weight it primarily, weight the inside handlebar. Note that the primary reason that you're weighting the inside bar is to initiate countersteer.
How can one get feedback when the (front) tire is about to loose traction?
If you've got everything weighted properly and you're lucky, the back will cut before the front does, at which point you've got a fraction of a second to stand the bike back up, or you crash. If the front goes first, you crash. A lot of knowing the limits of road bike tire traction comes from experience, and crashing.
What does "dynamic" mean in this context?
There's a lot more movement of your body on and over the bike on a trail than on the road. The more technical the trail, the more this is true. The "lean the bike, not the body" advice is a good rule of thumb, but it is not a one size fits all solution for mountain biking. There are so many different types of turns in mountain biking- fast, slow, bermed, off-camber, uphill, downhill, steep, flat, loose, rocky hardpacked, etc, and nearly infinite combinations of each. Many categories of turns deserve their own questions for cornering technique.
Is it customary to place the inside foot on the road in order to have three contact points and prevent tipping/sliding out?
Typically not during the turn. I've seen it done it the wet sometimes, but taking your foot out/off of the pedal during a turn will affect up your balance, especially on a road bike. Getting your foot out of pedal at the last minute is really hard, especially with road pedals.
Is the weight of the rider evenly spaced (chin over stem, butt over seat)?
Somewhat dependent on slope/incline and speed, and whether you're on the hoods or in the drops, but largely yes, this is correct.
Is standing up to gain additional "acrobatic" space i.e. freedom to more one's weight around rapidly ever used?
On a road bike, typically only for slow speed maneuvers. There are probably exceptions but I can't think of them at the moment.
What about slippery pavement - water, snow, sand?
Sloooow dooown. The more treacherous the riding surface, the more upright you need to keep the bike and your body.