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A year between apping for cards and a mortgage should be fine but you'd be better after verifying with your mortgage agent. The question is fairly general so we can only really provide a general answer.
Hard pulls do have a negative impact but the effect falls off fairly quickly. It's the hit to AAoA that takes more time to recover from. You can calculate the impact on AAoA before making your decision.
As stated above, the scores you mention are FAKO's. They could be close to your FICOs or they could be off by a bit. The only way to be certain is to get your FICOs.