Yes a minor can have a checking account, or a savings account. They can even get a debit card. The money in that bank account belongs to the minor. The account can be established as soon as the are assigned their social security number. If they are a newborn the account is generally set up as a joint account with a parent to facilitate transferring money into the account. For us the money was birthday gifts from relatives.
The IRS allows minors to receive small amounts of interest, or other unearned income, tax free. In 2015 that is up to $1,050, if they have no earned income. When bank rates were higher some parent's wanted to put all their saving under their child's name, of course in the eyes of the law the money belonged to the child and was only to be spent for items that benefited the child.
Credit cards are another matter because the CARD act in 2009 required lenders to only give credit to those under 21 who had proof of sufficient income, unless there was a co-signer.
You do have to be careful when talking about owning a house as minor. They generally can't sign a contract. You could gift the house to the minor, but if it was time to sell it the courts would insist on appointing a legal guardian to represent the interest of the child. That could add significant time to the transaction.