Having fought with negative film scans for many years, and having started optical RA4 printing recently, I would put the blame squarely on the developing and scanning service (except for the ugly white line sticking out of the boy's head in the first image and the strong back focus in the second image). You will see no grain/noise like that if you optically enlarge these negatives, whereas most negative scans will look like grain hell. Accept and embrace grain as something which is part of scanned negative film and switch to slide film if you want grainless. Not because slide film has less grain than negative film per se, but because slide film scans have less grain than most negative film scans. Scanning these negs yourself won't change that, quite to the contrary, minilab scanners are surprisingly good compared to common film scanners. You will find people online who claim they can scan negative film grainless but for some reason these folks are nowhere to be found in those labs we use.
The white lines running parallel to the film in the second image indicate scratches introduced during the development or scanning step. Check the negative strips for these and bring this issue to the attention of your lab. If they don't care, switch to another, more professional lab immediately.
Next is exposure: the definition of ISO speed says that with negative film you have about 4 stops below your metering before you have unstructured blackness. If you spot meter into shadow area, you will have great detail in these regions, too, but if you use center average metering for a back lit portrait, the face will lack detail and structure. Since the face is the first (and sometimes only) area we look at in a photo, it is crucial to have detail there and you must meter accordingly. Note that all these hints "I shoot it at EI 175.23" don't mean squat if you aren't told which areas are metered.
Next thing you must take into account is that C41 film was originally meant to be enlarged on photographic paper which had more or less a given contrast. This means regardless of scene contrast your images came out looking normal in the correctly exposed regions, blown out in the overexposed regions and as dark blobs in underexposed areas. There were few ways to alter contrast and these were generally not available to Joe Shmoe holiday shooter. Fast forward to digital scanning and it was suddenly possible to adjust contrast at will, and that's exactly what your scanning service did: they compressed the dynamic range until it filled but not overextended the dynamic range of the JPEG format. In a back lit scene you have huge contrast, so after contrast compression your scanned image inevitably lacks contrast and punch. Unless you can tell your lab to redo the scan in specific ways you must account for this when you shoot the image and avoid high contrast scenes. Which is a shame because negative film has huge dynamic range.
It takes some time to master this medium but it can be very rewarding if you get it right.