You will receive a letter from the Jarl of Falkreath offering you land when you are low level (7-9th?). Then you will have to do a kill the bandit quest for him, and you can buy Lakeview. You might be able to circumvent the letter and just go straight to the Jarl sooner? I have not tried it though. Perhaps someone else can say.
The house in the Pale can only be bought after you reach level 23, and once again you have to do a quest for the Jarl first. In this case you do not get a letter, you just have to go talk to the Jarl once you hit 23rd level.
The house outside of Morthal I am not sure about. I have not had a character buy it yet. I do know you will not get a letter for it either though, so you have to go talk to the Jarl and ask about buying property. Whether there is a level restriction or not I do not know.
Once you have a home, and you build the Main Hall and then the Bedrooms wing, you can adopt two kids. They will only sleep in the two beds in the Bedroom wing, even though you will have plenty of other beds in the Main Hall itself. Until you have those Bedroom Wing beds, you cannot adopt.