Chartjs-How to make dynamic chart with the next view? What libraries allows to customise exactly this like in my design?

You can create that type of chart in a simple way by using Highcharts.

In case of any problems you can get help on support channels: https://www.highcharts.com/blog/support/

Highcharts also has officially supported vue wrapper, which can be useful in your case: https://www.npmjs.com/package/highcharts-vue

You can start from:

Highcharts.stockChart('container', {
    series: [{
        data: [...],
        zones: [{
            value: 0,
            color: 'red'
        }]
    }],
    navigator: {
        enabled: false
    },
    rangeSelector: {
        inputEnabled: false
    },
    scrollbar: {
        enabled: false
    },
    legend: {
        enabled: true
    }
});

Live demo: http://jsfiddle.net/BlackLabel/vknsb7rw/

API Reference: https://api.highcharts.com/highstock/series.line.zones