Some comments regarding Q4 & Q5 based on past experience
a) Make sure when comparing assembly quotes, that they're for the same thing. I've had a client proceed with a cheaper quote (without discussing with me) and it turned out that component cost wasn't included. In the end the cheaper quote was slightly more expensive (but not by much).
b) Be aware of the MOQ cost on components sourced by the assembly house. While assemblers will typically have stock of common "jellybean" parts, they will also try get you really good bulk pricing on anything they don't stock as it makes the quote look more attractive per unit cost. What they don't always tell you upfront (often in the "fine print") is that you'll be responsible for paying for the full MOQ of the bulk purchases. I've seen this as high as $2,000 extra on a $10,000 order. Those excess components will be returned to you if you don't place another assembly order that will use them within a couple of months. If they're for export (e.g from China) they will often they'll be stored in a "bonded warehouse" as the duty hasn't been paid on them, and thus there is a deadline on exporting them.
c) Be aware of lead times. Again to get per unit costs down, they'll try find the best prices on components, but that may push lead times out by weeks if not months.
Re Q3, if assembling in China you need to work with a trusted manufacturer that sources components from trusted supply chain (e.g. Digikey). You tell them this upfront when getting the quote, and tell them you'll need documentation to prove it, and you'll be doing cross checks of batch numbers. It is a little tricky to enforce, but it has worked for me. Having someone on the ground who can visit the factory is very useful here. Generally the supply chain tracking it is only needed on the more costly or specialty parts. You can always supply the parts yourself, but this is painful when importing to China (very strict customs) and a dodgy company could still swap out the good parts you supply with cheaper, then resell yours.
Q1 is almost always yes, and for Q2 it is unclear what you mean.