All of the things you list can be done with Qlik Sense although it is not in a single "tool"-like feature. You do have to do some load script coding to achive for instance 1 and 2. 3 and 4 can be done directly: Mixed data type field will indicate that it is mixed by not having the tags for $numeric, $date or any of the specific data type tags. Can be seen in the Data Model Viewer. Here you can also have statistics for how many distinct values and null values that could be very valuable.
If you're comfortable with Python or R they can be employed with libraries to support data quality inspection and data cleaning before you bring them into Qlik or during the load script process by using Qlik SSE:
A couple of almost random links to what is out there:
