How can I exactly get to know where to install the anchor points and also the exactly length of the lines of a geometric structure like those ones on the picture if I would like to realise this in real life?
If you wish to have both the length and angle of one/each of the lines without calculations, you can (Smart Guides are your friends, helping you to snap) ClickDrag between the top and bottom end Anchor Points with the Line Segment Tool, then Click an empty spot to see them (length and angle).
The PNG seems to show an irregular set of lines. If you wish to have the bottom Anchor Points equidistant, one easy and safe way without calculations is to use a blend:
1) Create either of the outermost lines,
2) Object>Transform>Reflect it and ClickDrag the copy by the top Anchor Point to snap to get coinciding Anchor Points (this way you are sure that they are same lengths and angles),
3) Object>Blend>Options, set the Spacing to Specified Steps = the number of lines in between,
4) Object>Blend>Make, then Object>Blend>Expand if you wish to have (a Group of) separate lines (you can Ungroup).
To get the actual length of the selected line (the Properties Panel only shows the length and width of the space the line inhabits) go through Window>Document Info and select "Objects" from the pull-down menu.