I’ll add the following:
About 1): downcuts are great to get a clean finish on the top edges, but then you may end up with sub-optimal finish on the bottom edges (the opposite of when using upcut endmills). I see you are cutting 1/8" thick material, you may have some luck using 1/8" compression bits at full depth (they have both an upcut section at the tip and a downcut section a bit higher up the flute, which can result in perfect finish on both the top and bottom edges. They did wonders for me to cut thin (and cheap/low quality) plywood, illustration here.
About 2): The feedrate can stay the same, as it relates mainly to the number of flutes (and indirectly to endmill diameter). However downcut have poorer chip evacuation, since they tend to push chips downwards, so when e.g. slotting they can end up getting packed at the bottom of the cut. I like to use a smaller depth per pass (than I would use for an upcut) when I use downcut endmills for that reason.
About 3): in addition to Will’s and Stephen’s answers I’ll add that for me shank diameter mostly helps to reduce tool deflection. But for cutting through 1/8" of wood, and assuming you minimize stickout and are not looking to optimizing your cutting time, a 1/8" shank will do just fine. I have a large variety of 1/8" endmills, fancy ones from Amana from the C3D store as well as cheap ones bought in 10-packs on eBay, and they all have their purpose (I will use the cheap ones for aggressive roughing or when trying out a new project the first time, since I won’t lose any sleep over breaking one or two, and then I’ll keep the Amana ones for when the prototype is OK and I want to proceed with the final cut)