"(1) Does birth control go against God design? Are we preventing the birth of “chosen” ones? (2)But then, is it irresponsible to have children if one can’t provide for them?"
Question 1 - my short answer here is "no" at least not any more than taking an antibiotic or have surgery to remove a tumor changes God's plan for you to die in a timely and appropriate manner.
The bottom line on this question (for me) is a simple one. God gave us a certain amount of intelligence to control things in our environment. We make machines, we discover drugs, we learn about sterile techniques - all of these things have certain risks and benefits associated with them. In the case of birth control, (There are several methods here and I am lumping them together for convenience, but rest assured, I do not consider abortion to be an appropriate means of birth control.) we have learned ways of keeping sperm cells and egg cells apart - while still engaging in sexual activity. I would argue that God's plan included providing us with a brain to figure this out.
Question 2 - Yes, I think it is somewhat irresponsible to have children if you cannot provide for them. People should think about the possible offspring they might be generating before engaging in sexual activity. Only engaging in sex in the context of a committed marriage relationship is the Christian ideal for bringing children into the world.
But, people do irresponsible things every day. We are, after all, human and prone to make mistakes. So, what then? Here I would argue in favor of two things - changed priorities, and adoption. Changed priorities in that the parents of this new life might need to drop other (good?) things in favor of seeking employment to provide for their children. If that is not possible, adoption provides a terrific way to place a child in a loving home that can provide for their needs. In fact, MPC runs an excellent adoption agency called The Miriam Project - we really DO care for these children in tangible ways.