Charged particles tend not to aggregate so if there is a way to make them charged it will help (this could also be done by making a charged coating). Also you should choose a solvent that disperses the particles well (e.g. a polar solvent for polar particles [for some biological particles you might not have much choice here though since e.g. proteins tend to aggregate when they are denatured]). Detergents also help to stabilize a suspension.
Nanoparticles aggregate due to attractive forces. So, the nanoparticles will stay separated if they repel each other. One of the easiest ways for that is to use charged species like citrate as capping agents as the nanoparticles will start to repel each other due to electrostatic repulsion between the similarly charged ions.
Using surfactants also stabilises nanoparticles in solution as they enapsulate nanoparticles and prevent the formation of bulk.
Both these techniques are quite well known. You can find it in any standard book or review on nanoparticles.
It depends on the agent you use. There is e.g. some lipids that are quite biocompatible. You can look into drug delivery articles as far as I know there are several biocompatible options.
It is true that capped nano-particles are useful for drug delivery, but at the same time, it designs the nano-particles morphology and unless you have the cap, no nano-particles will form. The famous example is the capping agent produced naturally by enzymes insides bacteria to eliminate the toxic silver ions by neutralization, make ions free valent sliver atoms and kick them out the cell. And this is a big obstacle to collect them without capping agent from this biological kitchen.
Yes they use the particles with the shell together for drug delivery (you can look for the term core-shell nanoparticles). You can just evaporate the solvent and then you have the powder (from my experience resuspension might be problematic [you can resuspend some particles but you often have some loss due to aggregation]) Spreading them on a surface can lead to separated particles which can be useful for characterization.