I assume before you started this process you were pre-qualified with a lender?? The lender should have reviewed figures with you, and should have given you a "Good Faith Estimate" (or GFE)?
Is the builder giving you an incentive to use their lender? If so, you absolutely want to see an estimate of their closing costs. Most builders will dangle an incentive in front of buyers (like $X paid toward closing costs or for upgrades). BUT...then they inflate those closing costs quite a bit. If I were you, I'd go back to whatever lender you were dealing with and get that GFE, and if it's the builder's lender, I'd go to another lender and get a GFE from them.
As far as completion date....The sales person at the builder should have explained how long it will take to have your home completed.
Sounds like you're not being represented by a Realtor. This is why I always tell Buyers that it's good to have a Realtor represent you as a Buyer's Agent ... even with new construction. The builder is looking out for their best interests, NOT yours.