if your design and welding is good 1/8" will work. some pics of what you are doing will help to answer more completely.
That depends how you design it. Without trying to be a smart ***, I think if you are asking the question, you probably don't have enough engineering / design experience to build it strong out of 1/8". Therefore I would err on the side of caution and use something more substantial like at least 1/4". It still depends on your design though. Maybe some more info would help get the answers you want. Pete
Aside from the design, I think the most important missing piece of information is what kind of engine/car are we talking about? Stock 4 banger or blown hemi?