Eggs are an emulsion that includes fat, protein and water. The addition of these can make the bread more moist and elastic, and the dough softer.
The cooking time and handling will need to be adjusted.
If a great many are added the dough may become more of a batter.
It will rise too quickly and will taste very yeasty...not in a good way.
The only thing that will happen is the mixture may be too moist, or the eggs will not cook properly if there are too many.
'French' toast
Yes, because pizza dough is pretty much bread, and bread has yeast in it.
Bread dough will become what is called "blown" dough. It will "blow up". Because of the gas bubbles produced by the yeast, it will keep growing until it has no structural integrity. It won't explode but may rupture and then will start turning into a puddle of goo. It also produces less than desirable looking bread and developes a bitter taste.
Yeast is important in bread making as yeast is the reactant with heat in the oven that makes it rise. It also releases Carbon Dioxide (CO2) which gives you the tiny holes in the bread. The yeast cells in bread dough ferment sugars and produce gas (carbon dioxide). This will make the dough rise. If there is not enough yeast, the dough will not rise sufficiently and become less fluffy after baking. Without yeast you get unleavened bread. With too much yeast the dough becomes very light, and in the oven will collapse. in both cases the bread is still completely safe to eat. The amount of yeast per bread is very much a matter of taste and varies from country to country.
Too much flour can cause bread to be heavy and dry instead of light and airy.
Dough for bread only heeds yeast if you want to make light fluffy bread. If you want to make "hard tack" or "zwieback" or "matzos" then you can forgo the rising agent (yeast). Yeast converts carbohydrates (sugars and starches) into alcohol and carbon dioxide. The alcohol evaporates and the CO2 gets trapped in the pockets of dough (thanks to a large degree to the gluten in wheat). These pockets of gas remain after baking making the bread light and tasty.
Neither is great, but of the two, whole wheat would be better. It is a little harder to breakdown into sugar so you will not spike quite as much or as quickly. Actually I've hear quite the contrary. Sourdough bread is sour due to lactic acid released by the bacteria fermenting in the dough. The lactic acid is what keeps the blood sugar from rising.
Excess sugar produces a very negative water potential and this causes water to move out of the yeast cells into the sugar solution (by osmosis)- the cells become dehydrated, they do not have enough water for cell growth (yeast cells are usually 90% water).
Lard is not needed to make yeast bread. You can make excellent bread with just yeast, flour, water, and salt for flavoring. If your recipe calls for shortening or butter, substitute the same amount of lard for each. (Except for brushing the tops of the dough; butter or egg wash still works best for that.)
As you knead dough many important things take place: the gluten becomes developed so the bread can rise to its fullest, air bubbles are incorporated into the dough necessary for the dough's rise and the ingredients are redistributed for the yeast to feed on resulting in a more active fermentation. This enables the dough to expand to it fullest during the rising and baking steps.
The holes are gases from the yeast eating the sugar in the dough. These bubbles are what makes the bread light rather than solid like a cracker. As much as it may seem a bit gross, the gas is essentially yeast farts!
Bread making is a balance between the various ingredients. Too much or too little of any one of them alters the result. Too little water and the batch will not mix or knead properly, resulting in a hard lumpy unappetizing loaf. Too much and it will be sticky and glutenous and unappetizing.
It depends how thick the dough is and how much yeast is used.