Type of wood and darker spots  

That is white oak and the dark spots are due to iron and water. Oxalic acid will remove them. 

is there any other post where how to use this acid on wood is described ? Thank you for your answer

I used it ones and my spots got much less, despite not desapeared totally. You might find some description on the bottle.

Basically you put the acid with a brush generously over your spots and wait for an hour or two. Then you will see that the acid will bleach your spots. Then you can repeat the treatment until you get a desired condition.

Barkeepers Friend contains oxalic acid and can be used to bleach dark spots.  Here's a good blog post I came across recently:

https://www.finewoodworking.com/2018/10/10/remove-iron-stains-wood

Thank you !