Someone asked me these questions, I thought to share my answers in this blog.
How do we respond to atheism regarding Krishna consciousness which tend base itself on analysis and evaluation of hard evidences and thus discarding the idea of god and Krishna altogether through an objective eye?
Atheism basically stems from modern education and modern science because in science, the idea of God is not taught to students. Science as you say is based on evidence and its analysis. Evidence as per science is defined as that which can be observed and put to experimentation and from that experimentation derive mathematical constructs within Cartesian space. This is called empiricism or empirical science. If scientists cannot collect and subject evidence within Cartesian coordinates, then such evidence or theory is not scientifically valid. But God can never be a "subject" or be "subjected" to human control. God is always an "object" (never the subject). So unless scientists and their followers (atheists) give up this pride of subjecting evidence to test, they cannot and will never understand God.
So the first principle to understand God is to do the opposite of what atheists and scientists do - that is instead of "subjecting" evidence to human control, we "subject" humans to God's control. The idea, however, is the same. It is simply a matter of who is the subject and who is the object. Scientists have their "objective" such as research and grants and peer review papers. With this "objective" they "subject" evidence. If we want to understand God, we put God as the "objective" and we volunteer our self as the "subject" to be "subjected" to God's control. So when we become the evidence to God's experiment or plan, then from within our heart, that very God who is unscientific dogmatic idea will become a scientific truth or fact. The bottom line is - it is a matter of which methodology we want to pick but there is truth in both spheres, God and science.
On the road to spiritual path, how can we expand our spiritual roots while resolving dilemmas of day to day life. How to act more purposefully in our practical life?
The whole Bhagavad Gita was spoken for this purpose and obviously I cannot summarize all of it here. For us to solve our dilemmas of daily life, we simply have to connect our self back to our source who is God. Right now we are disconnected, hence we face dilemma, doubts and fears. When we connect back to Krishna or God, then all of our daily issues will be automatically resolved. So the answer to your question is simple, connect back to Krishna or God and stay connected (because you have free will to disconnect). Now, how to connect and stay connected is the reason the Gita was spoken. But basically Srila Prabhupada has given us few principles to stay connected always with Krishna. They are (1) chanting (2) listening to lectures by Srila Prabhupada (3) reading Bhagavad Gita (4) associating with devotees (5) eating prasadam daily cooked with love for Krishna. When we do these five things daily sincerely, seriously and without selfishness, gradually we will revive our lost connection with God and will be able to stay connected with Him always. In this connection, all of our material troubles will be resolved.