Magento – How to i edit default Magento 2 New Products widget template

The file you are looking for it here:

vendor/magento/module-catalog-widget/view/frontend/templates/product/widget/content/grid.phtml

If you place some dummy text here, you will see if on your home page. So if you want to edit this file further, you can copy it over to your theme.

To answer your question, at this point I have not found a .phtml or .xml that controls the product grids, they are all controlled by the styles based on css breakpoints. If you take a look at this file vendor/magento/theme-frontend-blank/Magento_Catalog/web/css/source/module/_listings.less you will see this:

.media-width(@extremum, @break) when (@extremum = 'min') and (@break = @screen__m) {
    .page-products .products-grid .product-item { width: 100%/3 }
    .page-products.page-layout-1column .products-grid .product-item { width: 100%/4 }
    .page-products.page-layout-3columns .products-grid .product-item { width: 100%/2 }
}
.media-width(@extremum, @break) when (@extremum = 'min') and (@break = @screen__l) {
    .products-grid .product-item { width: 100%/5 }
    .page-layout-1column .products-grid .product-item { width: 100%/6 }
    .page-layout-3columns .products-grid .product-item { width: 100%/4 }
    .page-products .products-grid .product-items { margin: 0; }
    .page-products .products-grid .product-item {
        width: 23.233%;
        margin-left: calc(~"(100% - 4 * 23.233%) / 3");
        padding: 0;
        &:nth-child(4n+1) {
            margin-left: 0;
        }
    }
    .page-products.page-layout-1column .products-grid .product-item { width: 100%/5 }
    .page-products.page-layout-3columns .products-grid .product-item { width: 100%/4 }
}

which defines the breakpoints at when the grid will shift from 5 to 4 to 3. When I have had to change this around, I just do it in the styles, based on what I need, just change the math around to work with the design.

toHtml() return block's html output

Process

\vendor\magento\framework\View\Element\AbstractBlock.php

    public function toHtml()
    {
/* dode */
            $this->_beforeToHtml();
            $html = $this->_toHtml();
            $this->_saveCache($html);
/* dode */
        return $html;
    }

Next this goes to \vendor\magento\framework\View\Element\Template.php

protected function _toHtml()
{
    if (!$this->getTemplate()) {
        return '';
    }
    return $this->fetchView($this->getTemplateFile());
}

Renders block html. and $this->fetchView function retrieves the block view from file (template).

Assume you know templates are using block functions and blocks extends core classes ( Template.php or AbstractBlock.php not in all cases ).

The data is populating by using toHtml()

Hope this helps.