Draw an arc/circle sector in QML?

Yes, using Canvas (and Context2D):

import QtQuick 2.3

Rectangle {
    width: 400
    height: 400

    Canvas {
        anchors.fill: parent
        onPaint: {
            var ctx = getContext("2d");
            ctx.reset();

            var centreX = width / 2;
            var centreY = height / 2;

            ctx.beginPath();
            ctx.fillStyle = "black";
            ctx.moveTo(centreX, centreY);
            ctx.arc(centreX, centreY, width / 4, 0, Math.PI * 0.5, false);
            ctx.lineTo(centreX, centreY);
            ctx.fill();

            ctx.beginPath();
            ctx.fillStyle = "red";
            ctx.moveTo(centreX, centreY);
            ctx.arc(centreX, centreY, width / 4, Math.PI * 0.5, Math.PI * 2, false);
            ctx.lineTo(centreX, centreY);
            ctx.fill();
        }
    }
}

I actually took the code for this from this answer, as Qt's Canvas implements the HTML5 Canvas API. This makes it really easy to find examples on the web; just search for "draw pie slice blah html5 canvas", for example.

For the mouse detection, you'll have to brush off your maths skills...

... or just steal the code from here. :)

Note that Canvas only repaints when it's resized, or when requestPaint() is called, so if you want to change the colour of a slice depending on the mouse position, you'll need to call that function to see the colour change.

Draw it using qml, you don't need the canvas. As a guideline I usually go through Qt's examples before deciding on an implementation. The code below can be found in "Shapes" example.

import QtQuick 2.11
import QtQuick.Shapes 1.15

Shape {
    width: 120
    height: 130
    anchors.bottom: parent.bottom
    anchors.right: parent.right
    // multisample, decide based on your scene settings
    layer.enabled: true
    layer.samples: 4

    ShapePath {
        fillColor: "black"
        strokeColor: "darkBlue"
        strokeWidth: 20
        capStyle: ShapePath.FlatCap

        PathAngleArc {
            centerX: 65; centerY: 95
            radiusX: 45; radiusY: 45
            startAngle: -180
            sweepAngle: 180
        }
    }
}

Use charts http://doc.qt.io/QtCharts/qtcharts-qmlmodule.html

import QtQuick 2.0
import QtCharts 2.0

ChartView {
width: 400 
height: 300
theme: ChartView.ChartThemeBrownSand
antialiasing: true

PieSeries {
    id: pieSeries
    PieSlice { label: "eaten"; value: 94.9 }
    PieSlice { label: "not yet eaten"; value: 5.1 }
}
}