I'm using Grid table in Vaadin for data representation. 
For that I'm trying to figure out the following two issues:
1.) How to disable the sort function in the Header of each column
2.) How to set the color of one column in a Grid table
First of all, I find the Vaadin docs a good place to start looking for help. For the rest of the exercise, suppose we have a Grid with 3 simple columns c1, c2 & c3:
Grid grid = new Grid();
grid.addColumn("c1", String.class);
grid.addColumn("c2", String.class);
grid.addColumn("c3", String.class);
1.) How to disable the sort function in the Header of each column
Iterate through each column and set its sortable property to false:
for (Grid.Column column : grid.getColumns()) {
    column.setSortable(false);
}
Or just get that one column you want and set its sortable property:
grid.getColumn("c1").setSortable(false);
2.) How to set the color of one column in a Grid table
Similar to how it was done with the table, you need to define your CSS style in your theme:
@import "../valo/valo.scss";
@mixin mytheme {
  @include valo;
  // Insert your own theme rules here
  .v-grid-cell.green {
    background: #33BB00;
  }
}
And use a CellStyleGenerator to apply the style to your desired column:
grid.setCellStyleGenerator(new Grid.CellStyleGenerator() {
    @Override
    public String getStyle(Grid.CellReference cellReference) {
        if ("c1".equals(cellReference.getPropertyId())) {
            return "green";
        } else {
            return null;
        }
    }
});
Which should generate something along the lines of:

Here is a small supplement to Morfic good answer:
1.) How to disable the sort function in the Header of each column
Grid asks the Container if a column is sortable (see appendColumn-method in Grid). If you want to disable sorting for all columns, you can override getSortableContainerPropertyIds in your Container and return an empty collection:
container = new BeanContainer<String, Dive>(Dive.class) {
            @Override
            public Collection<?> getSortableContainerPropertyIds() {
                LinkedList<Object> sortables = new LinkedList<Object>();
                return sortables;
            }
        };
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