10.3#14

I am not understanding the first 2 parts of the question, can you please
rephrase it or somehow explain what it is asking for? Thank you.

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First of all, reading the chapter we are covering is very important.  You should read section all of section 10.3 in before you attempt the problems.  Especially you should read pages 554 and 555.

The implication of the problem is that F can be written as the sum of a part that is parallel to v and a part that is perpendicular to v.  But this comes from the notion of the projection Proj_v(F) of F on v:
 this IS parallel to v.  In addition F-Proj_v(F) is perpendicular to v, in fact the Proj_v(F)  is defined as the unique vector w parallel to v that makes  F-w perpendicular to v.  These give you the two vectors you need.