How to verify authenticity of smaller LEGO parts?
I have many 1*1*2/3 slope


On this piece the LEGO marking should be seen on the flat, semicircular part on the bottom: 


  Dark green - 3 with no number, n.o 31, n.o 3, n.o 5


I'm sorry, but I can't identify this piece, a photo would be helpful here.


  Red/brown - n.o 29, 2 with n.o 15.


Just like here


  Trans orange and red - 8 with different or no n.o


Or here.


  Also with the 1*1 round brick and nose cone - are there ANY markings usually?


Yes, there are, but they are quite tricky to find. On the 1x1 round, you should be able find the marking on the inner side of the top ring, facing down: 

While on the cone, it is similarly on the underside of the flat ring, but close to the bottom, so easier to see: 


  Also with the weapons and tools - I have many with a (C) but some with nothing...


These are quite broad categories, so if you have any specific pieces, I'd love to help you :)