[Solved]-How to create tooltip in highcharts map on click over a country...?-Highcharts

The plugin below should solve both of your problems:

(function(H) {
    H.Tooltip.prototype.hide = function() {};

    H.wrap(H.Tooltip.prototype, 'refresh', function(proceed, point, e) {
        if (e && e.type !== 'mouseover' && e.type !== 'mousemove') {
            this.updatePos = true;
            proceed.call(this, point, e);
        }
    });

    H.wrap(H.Tooltip.prototype, 'updatePosition', function(proceed, pos) {
        if (this.updatePos) {
            this.updatePos = false;
            proceed.call(this, pos);
        }
    });

    H.addEvent(H.Point.prototype, 'click', function(e) {
        e.point.series.chart.tooltip.refresh(e.point, e);
    });
}(Highcharts));

Live demo: https://jsfiddle.net/BlackLabel/3e4cvz2m/

Docs: https://www.highcharts.com/docs/extending-highcharts/extending-highcharts