Vectors scale to any size without losing sharpness, which is exactly why so many places refuse to accept them. Email clients, older presentation software, most social platforms and many marketplaces all want a raster image. Rasterising to PNG at the size you actually need gives you a file that works, with transparency preserved.
Export at the largest size you will actually display, then at twice that if the image needs to look sharp on high-density screens. Unlike raster sources, there is no penalty for choosing a large size other than file weight, because the vector holds full detail at every scale.
Yes. PNG supports alpha, so anything not painted in your SVG stays transparent in the output.
SVG text elements reference fonts by name, and the renderer can only use fonts your browser actually has. Convert text to paths in your vector editor before exporting if the typeface matters.
Not meaningfully. Rasterising discards the vector geometry permanently. Keep your original SVG as the master file.