Question 1062306
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Regarding your questions #1 and #3, see these links


http://www.cut-the-knot.org/triangle/tr3.shtml

https://answers.yahoo.com/question/index?qid=20110520005044AAQiQMO 

See also the book "The secrets of Triangles" by Posamentier and Lehmann, 2012, ISBN 978-1-61614-587-3, Example 14, p. 238.



Regarding your question #2, see this link

http://www.qc.edu.hk/math/Junior%20Secondary/Median.htm 

and also the same book, Example 17, p. 247.



You can search for this book in your local library.



Also, you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A>

in this site. 


In this online textbook, there are lessons on basic construction procedures in Geometry under these topics:


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Geometric constructions using a compass and a ruler. Basic operations</U>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Geometric constructions related to parallel lines</U>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Geometric constructions related to circles </U>