The floor sinking would indicate that the floor fill wasn't properly compacted or was of poor quality. The cracks are probably due to the foundations settling, again this would indicate that the ground under the foundation wasn't properly compacted prior to pouring or that the foundation trench wasn't taken down to suitable bearing. A structural engineer is what you require.
You will need a survey to be carried and a list of remedial works which will have to be designed by the engineer. While the civil eng might know what is causing it and mightknow what to do to rectify the problem the chances of him giving you design is very slim as he will have to stand over it with his PI. It is a structural engineers job and for something so potentially so serious you shouldnt take any chances
As i said the civil eng might be able to comment but structural issues are not (or might not be) his expertise , does he/she have insurance? Are they giving advise or designing a remedy?
Civil Engineering covers a wide range of diciplines, including structural mechanics so it is not clear to say whether the civil engineer you're talikng about is qualified to advise or not. If they work in structural design for a consulting engineers practice then their advice is probably right. If they design roads or drainage systems then possibly not.