Without starting a thread if a sweetener should be used or not;
1. Is is agave nectar or Trimoline Inverted syrup a one-one replacement for honey in a dough recipe?
2. Does yeast prefer sucrose or fructose?
3. Maybe simple white castor sugar or demerara sugar in the raw are the better options?
According to Wikipedia, some brands of Agave Nectar have different Fructose to Glucose ratio's so it may be difficult to answer.
Agave nectar consists primarily of fructose and glucose. One source gives 92% fructose and 8% glucose; another gives 56% fructose and 20% glucose. These differences, it is presumed, reflect variation from one vendor of agave nectar to another
Those are tough questions to answer because there are so many variations in the products involved. They all start out their lives as natural products and, as such, they are subject to many normal variations in term of sugar content, percents of the various constituent sugars (like sucrose, fructose and glucose), carbohydrate content, and also in their water content, all of which can vary from one production batch to another. These variations also make it difficult to compare one sweetener with another in terms of sweetness (like honey with agave nectar). This tends to show up most noticeably in the recommendations you see on how to substitute one form of sweetener for another. And the ranges of amounts to use can be quite wide. It also doesn't help that the purveyors of particular sweeteners, whether it is honey, agave nectar, molasses, maple syrup, malt syrup, or whatever, tend to recommend that one use more of their product than might actually be necessary. All of the above factors do not instill a lot of confidence in how you should use those sweeteners.
As to your particular questions:
1. The advice I have seen most often for substituting agave nectar for honey is to use the same amount of agave nectar as honey. However, if that is done, you have to make adjustments in the formula hydration due to the fact that the agave nectar is thinner in consistency than honey--because agave nectar typically contains about 25% water and honey is about 18% water. You can replace the honey with 18/25 = 72% agave nectar but you may have to play around with the agave syrup some more to get the desired final degree of sweetness, especially since agave nectar and honey do not taste the same even though they are both sweet. If the agave nectar is one with a very high fructose content, it might also be prudent to increase the amount of yeast to compensate for the slower rate of metabolism of the fructose. Otherwise, the fermentation may not proceed fast enough in comparison with honey, which typically contains 41% fructose (and 36% glucose).
The advice I have most seen with respect to substituting invert sugar syrup for honey is a one-for-one replacement. However, invert sugar syrup is sweeter than most other sweeteners, and I would guess that would apply to honey also, because it is made with cane syrup, which is the first stage of production. Again, you will usually want to make adjustments in the formula hydration to reflect the fact that invert sugar syrup can typically contain more than 25% water. You will also want to do some testing to determine how much to use to achieve the desired degree of final sweetness. Invert sugar syrup is usually a foodservice product although the Tate & Lyle Golden syrup imported from the UK is available at the retal level in some stores in the U.S., and also online, and may represent a good substitute for commercial invert sugar syrup.
2. I would say that yeast prefers sucrose over fructose. Sucrose contains both fructose and glucose. During fermentation, the acids of fermentation and also enzymes in the yeast cleave the sucrose into fructose and glucose. Glucose is preferred by yeast over the fructose mainly because it is in a form to be immediately metabolized by the yeast. The fructose eventually is transformed into glucose but it takes time for that to happen. Where fructose shines is that it is about 1.6 times sweeter than sucrose and, as a reducing sugar, it is a major participant in the Maillard reactions. As a result, you will get a lot of crust coloration where fructose is involved. For blue agave syrup especially, which I understand is the type of agave that is highest in fructose, I would expect to see good crust coloration. Maybe Don can comment on whether that is true.
3. Caster sugar, which I believe is a British term, is a more finely divided form of regular sugar. Demerera sugar (raw sugar) is a more natural and less refined, "purer" version of table sugar. I have not seen caster sugar in any store near me, and I have never used it, but if it is used as a substitute for honey, you will have to determine how much to use, given that it is such a fine grained sugar. Since honey and ordinary table sugar are often substituted for each other (subject to the need to make formula water adjustments), I imagine that the same applies when substituting demerara for honey. However, whether caster sugar or demerara sugar is used, you will want to increase the amount of the formula hydration to reflect the fact the you are losing the water in the honey.