@salmonmac, really, you’re calling me a crocheter now?? You have raised my status beyond my ability! Haha!
@Stella.b I think what you are seeing is the difference between a row worked on the right side and a row worked on the wrong side. The right side row the chain of 3 looks like a chain, the wrong side row, or return row the chain of 3 shows as the back of the chain. I this you are seeing the right side chains as raised and the wrong side chains as recessed - this is as you said every other row.
If you zoom in on the pattern photo it does have some undulation to it and perhaps more easy to see on the orange colour yarn insert photo where the very top chain looks chain-like (as this is the right side being worked) but the chain below looks a little recessed and more knotty rather than v chains.
I’m personally not so keen on the look but this is how crochet is when worked back and forth.
As for whether it is a UK or US pattern and whether it would be a double crochet or a triple crochet… the link salmonmac has given is a good source, look through your pattern to see if there are any clues as to whether it is UK or US terminology.
Another way to work it out is to consider the turning chain, how many chains are used to replace the first dc/tr.
I don’t see that swapping dc for tr would cause the raised rows you’ve mentioned. It would only change the size of the rectangle made. The only point where it could distort the shape is at a turn if the turning chain isn’t long enough to be equal to the stitch used. I tried to zoom in on the split where the turn is but can’t work out what is there. If you want you can increase the chain at the turn to equal the tr you want to use.
If you don’t like the raised and recessed rows you might consider working the whole skirt in the round so you are always looking at the right side and never turning. You would need to make it without the split or could find out if crochet can be cut (like steering in knitting) I would imagine this is possible, crocheting along where the split would be to catch all the stitches and then cutting, but I have no idea how to do it. It’s just an idea.
You could also try a small swatch with the dc instead of the tr and see if you prefer how it sits.
I hope something here is helpful.