what I was wondering was if I could use wood glue and dowels to secure everything together?
Normally that would be fine but there's a potential problem with the design of this piece because the wood meets in a corner.
Due to the width of some components you have to take wood movement into account if this is made from solid wood as you intend and not from a board material like plywood or MDF.
Wood movement generally
Solid wood absorbs and loses water through the seasons as humidity goes up and down and as its internal moisture level changes it expands and contracts across its width. If the expansion of one piece doesn't match that of the piece it is attached to it's a problem.
You must allow the wood to move or stress builds up and it can cause warping or cracks, either along the glue joints or in the wood itself.
Wood movement here
When two pieces are joined at 90° usually they each expand and contract in the same direction (a classic example being a shelf and the side of the case in a standard bookcase). But here, because of the corner design the grain in the shelves is in the correct orientation with one side panel but at right angles to it on the other.
Because of this you can glue and dowel the shelves to the left panel in your image, but the shelves need to be allowed to move relative to the right panel so some other fixing method needs to be utilised there (and the shelf can't be glue on that side, except in towards the corner).
How you can ignore it
Or you could make your shelving unit from plywood instead and simplify things for yourself. Then you can glue and dowel the whole thing together without worrying about movement.
Secondly; I was thinking of using pine, but in my research found out that it is a very soft wood, would this be okay provided it would only carry small light objects (Keys, pens, rubiks cubes, Nicolas Cage bobble head)? What would be a better alternative taking into account that I want to use a light (colour wise, not weight) wood?
It's not very soft. It is soft, but usually not intolerably so. I should mention there are many different subspecies of pine and some are actually reasonably hard in comparison to the usual stuff you'd buy in a big-box or similar. But even the softest kind is still perfectly usable for something like this, and in fact could be used for a kitchen table that will see regular use (as many such projects posted online show).
And lastly; What sealer do I use? I saw that there really isn't one correct answer for this. What I want is a clear, dry curing layer to protect the wood and keeps its colour. So an acrylic lacquer maybe?
This is as much a matter of personal preference as anything. If you're happy with the cost and application method of an "acrylic lacquer" (I use quotes here because that can be a range of things) then go with it, it'll likely give you exactly what you're looking for.
Note however that you can't stop pine from changing colour due to exposure to light and oxygen. If the finish you use has UV blockers included in the formula those can delay colour changes in wood but the protection is not permanent. Eventually any area of the pine not shielded from light by the items placed on the shelves will darken a little bit and go slightly more yellow, which are the standard colour changes for pine.
