Yep, that is mushrooms growing in the kitchen!
While we have had a very rainy season, mushrooms should not be growing wildly inside the kitchen. Also, if you see water coming through a foundation or retaining wall, please have it checked out by a professional contractor or home inspector. Having a home inspection is the number one way to find out hidden defects on a home prior to purchasing. I work with some of the best home inspectors in the business and would love to give you a referral.