Sorry for the late reply, I was googling something similar to your question and found this. I play several Grilled Cheese sims and have also read way too much on the Sims wikia, so those are my references. Q1 I'll have to try to pay closer attention to in my game and update you - I play TS2 Ultimate Edition (all expansions) at the latest version. I've seen this glitch listed elsewhere as well, but am not sure. Worst case scenario, test it yourself then get your Sim to exercise or use a Witch Sim to cast Corpus Athleticus to fix any accidentally gained weight.
(EDIT 2: It does not appear to work. It appears that conjuring a grilled cheese sandwich will keep the fitness bar about the same, but actually making food and eating it definitely dropped the Fitness bar somewhat.)
Q2/Q3 - Grilled Cheese paintings are basically the same as other paintings- they are not automatically considered masterpieces and are dependent on the Creativity skill. As such, the Grilled Cheese paintings are mostly cosmetic. If there is a difference in price, it's not noticeable. The main benefit of Grilled Cheese secondary aspiration would be that your Sim becomes happy after making Grilled Cheese sandwiches, so if you're running a store or restaurant which sells Grilled Cheese, this can help keep your Sim's mood very high.
If you're looking for secondary aspirations to help the primary aspiration Fortune, most aspirations will help you in one way or another. I'd recommend the Pleasure aspiration, as it allows for you to write Restaurant Guides influenced by how often your Sim goes out to eat. The knowledge aspiration will allow you to build skills more quickly through "Eureka!" and therefore will allow you to get to Creativity 10 or other needed skills faster. If you're running a Sim business, you can sell Grandma's Comfort Soup from the secondary Family Aspiration- your Sim makes simoleons, and other Sims have easier access to a food which cures illness. Popularity and Romance don't create ways of making money, but do allow for faster friend building, which is good for helping you get promotions.
Q4 - There is no cooldown for summoning Grilled Cheeses, but it causes a drop in the Energy mood. You can essentially convert Energy to Hunger this way and also boost your Sim's aspiration, while also saving Simoleons on food. The drawback is that in order to get the ability to summon sandwiches, you have to have Grilled Cheese as your PRIMARY aspiration. GC Sims only receive wants and fears related to Grilled Cheese, not generic wants (unless they're on a Date, in which case they receive Date-related wants.)
Q5 - Because it converts Energy to create sandwiches, I don't THINK sandwich creation occurs autonomously- at least, I've never seen it happen even with a really hungry Sim. It would be really bad if you were playing a Sim with Low Hunger and Energy and the Sim decided to pass out by creating a sandwich! If I do notice this happen, I'll let you know, but I've never seen it.
Hope that helps!