All of the High Priority ALMA projects from previous and current cycles are listed at the "High Priority Projects" page of the Science Portal. Priority C, or "Filler", projects are not listed here.
Targets are not listed at the Science Portal but by querying the ALMA Science Archive it is possible to see all ALMA observations that were successfully observed and archived. You can search by target name, position, project code, etc., and the returned meta-data include some specific details of the observation, such as observing band, frequency, channel spacing, etc.. If the proprietary period for the observation is over, then you will also be able to retrieve the archived data products. Note that on the query results page, you can use the little double arrows found on the right of the Result Table to add columns, or you can drag and drop columns under the Columns section at the bottom of the page. The query will return all matches for observed data regardless of priority (i.e. either "High Priority" or "Filler").
If you want a list of all science observations currently in the archive, go to the Knowledgebase article "How can I get a full list of everything ALMA has observed?".