In text listing style - how to use? Any downsides?
Yes it is a good/acceptable style. At least in the fields where I have looked the format is standard. in fact bullets or numbered lists should be used more sparingly and I think the following is a good guideline: use bullets/itemization when there is a lot of text going into each. 'Lot' in this case is a complete sentence or more. Use the format you mention when you need a word or partial sentence for each item.
there are several ways to do this you can use 'i)' or '(i)' or (1)' or '(a)' etc. The choice may differ depending on what else you have in your paper. If you have figures that contains several panes, for example, a, b, c, d, you may decide to use Roman or regular numerals for your lists. if you have several lists you should avoid repeating the same item descriptor and, for example, use Roman numerals for one and Arabic for another.
This depends on the context. you should place them where it is appropriate to read them. this means before each part of the construction. In your example you have divided everything into separate sentences but I think you should make a construct with semicolons instead: "There are three things of importance: (1) thing A; (2) thing B; and (3) Thing C."