How big is the image produced by the periscope compared to the size of the object

As long as both mirrors are set at 45% and the same size then you see the same as is reflected in the upper mirror 

Put a lens in the middle of the tube 

? 

We use mirrors when we drive cars ect 

Normally they are set across from a concealed entrance or one that is hard to see both ways like the inside of a hairpin bend. Sometimes only to help in one direction. 

Sonar which is sound waves that are sent out at a set rate then reflected by objects. The longer the gap between the two the further away it is, They still use periscopes to target boats though. 

The periscope can only reflect what is outside so if you could see it because there is enough light then Yes. If you could not see it because it is dark then No unless you get into Info-Red light or Image Intensifying systems as well