I'd love to make a rusty texture for specific part of my model (look at the picture), through texture paint, but I don't know how. It seems pretty lenghty and hard for me, in case of making it manually. So my question is - is there any easier way to make rusty texture only for part of my model?
You can make use of the Brush Mask textures with either a cloud, stucci or musgrave procedural texture set to View Plane, and Rake and Random in the texture mask brush settings in the tool bar. Using this, select your color under your brush with S and then set your brush blend mode to 'multiply' and lower the strength a bit. You can knock in some textured spots, and then switch your blend mode to 'screen' or 'add' to break this new textured area up with some illusion of depth. If it gets too strong, switch back to 'mix' blend mode and tone it down.
Using photo textures as a reference is actually best here, looking at the kinds of patterns that occur with the oxidation. Sometimes you just get pits showing up from under the paint, sometimes you have a whole area of voronoi-like shading aroudn deep wells. As the painter, you are the one in charge here.