If you want to use GetFeatureById, the id should be a number for example "1", "5" etc. The 2nd parameter is which column you want to read, the value can be found in the feature.ColumnValues.
I think you should want get the feature based on your column "UID", so the API should be:
Feature feature = shapeFileLayer.FeatureSource.GetFeaturesByColumnValue("UID", "PR71_1");
You can refer the sample: 9288.zip (99.4 KB)
Wish that's helpful.