順次: using ready rooms and displaying completed products
Read the order of using rooms as each becomes ready and displaying completed products, keeping readiness separate from ranking or a finished display.
Using rooms as they become ready
準備が整った部屋から順次利用を始める。 says that rooms will begin to be used in order as each is ready. 順次, read じゅんじ, describes sequential processing, while 準備が整った部屋から supplies the readiness criterion.
That criterion does not establish that every room is already ready. Preserve the planned start of use as the rooms become ready rather than a report of completed use.
Products to be displayed in sequence
完成した商品は順次店頭へ並べられる。 says that completed products will be displayed in the store one after another. 完成した商品 identifies the products as completed, while 店頭へ並べられる supplies their passive display relation.
The objects are products and the location is the store. Do not replace them with artworks in an exhibition or report that every product has already been displayed.
Processing order and readiness
Using rooms and displaying products are separate cases of sequentially handling the stated ready or completed objects. 順次 does not turn this into performance ranking or numbered card order.
The room sentence explicitly prioritizes rooms that are ready. The product sentence gives successive display without naming which product will be first.
Does beginning to use ready rooms 順次 mean using higher-ranked rooms first?
Show the answer and why
No. It means beginning use sequentially according to readiness. The other example concerns completed products to be displayed in a store, not artworks or performance placing.