Just bought a house 4 months ago (US). Wanted to refi, but couldn't because my credit dropped... Is this normal? How best to get back to excellent credit?

So I bought a nice house 4 months ago in the US. 1.2 million, 30% down. Going to do a remodel soon. My Fico credit score was 814. I was able to get a deal of 3.65% APR on my 30 year loan.

Last week, my friend's financial advisor calls me, says there was a one day drop in rates, and I can refi at 3.25%... Anyway, I tried to get a rate lock and am shocked to find my Fico score is now 725, too low to get the great rate. :(

Only real change in finances was buying the house--can that drop a credit score almost 100 points?

From the report, no mention of many details... It looks like I got dinged because I have only 1 credit card (I always pay it off, but it has a low limit of 12k), and also because I've had too many credit checks. I've been meaning to get a new credit card anyway, but will this hurt or improve my credit? I want to get back above 750 in case the rate drops again I can jump on it.

The whole credit score thing is poorly designed and opaque. Any advice would be appreciated.

Thank you!