Greetings from Syncfusion.
Query 1: In my first column, I have two cards (the first one and the very last one) which are special and I don't want to be able to move them
You can achieve this requirement using the AllowDrag property in the KanbanColumn. Please refer the below reference link.
Query 2: I have been trying to cancel the dragging of the other cards above and below the special cards
You can restrict the card transition from one column to another column using the Category and AllowTransitions property in the Kanban. Please refer the below reference link.
We have prepared a sample for the above queries, please download it form the following location.
Please let us know if you need further assistance on this.