Yesterday I was playing a video game with some of my guy friends when the topic of dating came up. One of my friends proceeded to tell us that his parents had strict rules about dating, such as: He's not allowed to date until he has a job, car, and his own place and the girl has to be chasing God's heart as fast if not faster than him.
I feel sorry for your friend. Whilst I do understand their parents' intention, I completely disagree with it as being excessively exaggerated. A job and a car are things which you should probably have by the time you get married, but, in my opinion, this does not mean that you cannot start dating much earlier. Nothing in the Christian idea of dating clashes with studying at university or with being still dependant on your parents, since dating is, as I see it, only a preparation for a likely (but not yet certain) marriage.
As for his own place, I disagree even more; as I see it, you should probably get your own place by the time you get married, not years before that. Genesis 2:24 describes the man leaving his parents at the time when he is united to his wife (marriage), not even before dating.
I am sorry. I know that this was not your question, but I felt that I really had to express my opinion.
So my question is this: How do you gauge the speed that someone is chasing God's heart? Are there particular signs that show how fast someone is chasing God?
The entire behaviour of the person should reflect how ‘fast’ he/she is ‘chasing’ God. (These are terms which I do not like to use; to be accurate, we do not ‘chase’ God; we follow him, we walk with him.) If Christ is in someone, that person is a new creation entirely (2 Corinthians 5:17), so every aspect of their life should reflect their relationship with God.
Do not look for ‘particular signs’ of the guy you looking for: see the big picture. Hang out with him; find out more about him; inquire him about specific ways in which he uses his life to glorify God (for example, whether he goes to church every week, whether he reads the Bible, what church ministries he is involved in…); and analyse the way he behaves with you and with others.
There is no specific guide. You should look into every visible aspect of his life and determine whether a Christian would behave like that.