Say I have a red object. I fill it blue with paint bucket. But I want the final color is blue+red=purple, not blue. And if the object has gradual red, then the final color is gradual purple as well. Is there a way to do so?
You can use layer blending modes in Inkscape to overlay one colour over another. You may have to experiment with these to find the optimal blend mode.
However, what you are suggesting is generally a bad idea if your intent is to create a working SVG for the web, or perhaps even if you are outputting as PDF.
If you use multiple layers/blending modes (see *note below) to change colours of underlying objects, you will find that different browsers may render these differently. Support for some of these is a bit flakey in some browsers, and probably totally non-existent/messed up for PDFs.
Not only that, but using the Paint Bucket tool creates additional filled objects, which will increase the file size of your SVG. and could possibly also affect rendering times in browsers.
Instead, it's better to keep the design as simple as possible: that means shapes and paths with strokes and fills applied directly to each. Don't be tempted to use layers/layer blending modes/effects.
*Note: These are absolutely fine if you intend to output as a raster image.