A joist under a supporting wall doesn't sound right.
Most likely (depending on age of the house) a bearer that has been fixed to a load bearing wall.
Water coming though an air brick doesn't sound right either
Its a fairly common problem. When houses are built air bricks tend to sit a decent way above ground level which means water cannot run into them. Over time the ground level is built up and people either don't realise or don't care that water can now enter the house through the air bricks.
The worst example I've ever seen of this was when I had to put right a floor structure that had rotten because the client had decided to lay a new patio himself on top of his old patio. Somehow he mistook an airbrick for a drain and the fall on his new patio directed ALL of the rainwater that fell onto said patio into the airbrick. Its fair to say his wife was a little upset with him.