Most of that info is determined by your credit score, among other things.They can check your Fico score (soft inquiry) without actually pulling your full credit history, but for a mortgage I would think they would have to pull a hard inquiry (full history).So I think it would be impossible, or at least not likely, that they would be able to give you enough info so you can compare without them pulling your full history. They may be able to give you a "range" of what your rate and closing costs is likely to be just from your Fico.Edit: Yes they will both pull your credit, but 'shopping around' for mortgage and car loans counts as 1 inquiry and doesn't hurt your credit score much at all.
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