The shutters won’t do it by themselves so you will still need blackout drapes along with the shutters . As for a clash I would have no idea unless you showed the house. IMO the shutters are so not 1900s why worry about anything else you do. Also your decor is quite Scandanavian so you will need to be careful of the look of the drapes that of couse will go from ceiling to floor , maybe a nice linen with a blackout liner I think the drapes are the only thing that will give you want.

I usually use blinds for the actual blackout and then the drapes added. If you post a pic of your bedroom you will get more help.

Skip the draperies. They're always going to look odd with the different heights in your room. Do blackout shades or blinds. Look for the type that has "side tracks" or "side channels" to block out the annoying light that comes in on the sides.

Yes, they do! With the light blocking of the blackout fabrics, the sunlight that gets amplified by the glass windows (creating a greenhouse effect) is stopped at the window level, preventing it from further heating up your living room, bedroom, etc. We also have several other ideas in terms of heat blocking!