Breakdown of Я полностью согласен с вашей точкой зрения.
я
I
ваш
your [formal/plural]
с
with (also со)
согласен
in agreement (short form)
Questions & Answers about Я полностью согласен с вашей точкой зрения.
Why is согласен used instead of a verb for "agree", and how does it affect the rest of the sentence?
In Russian, "to agree" is usually expressed with the short-form adjective согласен (literally "in agreement"). When you agree with someone or something, it is followed by the preposition с plus the Instrumental case. Here, that gives us the Instrumental phrase с вашей точкой.
If a woman is speaking, does she also say согласен?
No. Since согласен is a short-form adjective, its ending changes to match the gender of the subject. A female speaker would add an -а and say Я полностью согласна.
What cases make up the phrase точкой зрения (point of view)?
точкой (point) is in the Instrumental case because it follows the preposition с. зрения (of view / of sight) is in the Genitive case, answering the question "point of what?". It stays in the Genitive case no matter what happens to the word точка.
What is the dictionary form of the word вашей here?
The dictionary form is ваш (your). It takes the Instrumental feminine form (вашей) to agree with the feminine noun точка.