There are contribution limits to the traditional IRA in terms of the amount you can deposit. No, there is no maximum income limit for a traditional IRA. Anyone can contribute to a traditional IRA. While a Roth IRA has a strict income limit and people with incomes above it can't contribute at all, that rule doesn't apply to a traditional IRA.
You may still want to make a non-deductible contribution, either because you prefer to allow your investments to grow tax-free and defer income taxes or because you want to make a clandestine contribution to the Roth IRA by contributing to your traditional IRA and then converting it into a Roth account. Traditional IRAs don't have this rule, as do other types of IRAs, such as SEP IRAs and SIMPLE IRAs, which are often used by self-employed individuals and small business owners. While the traditional IRA shares many features with its newer sister, the Roth IRA offers tax incentives to save for retirement and, under certain circumstances, each of them is governed by a different set of rules. Initial tax relief is one of the main things that differentiate the rules of traditional IRAs from Roth IRAs, in which taxes are not allowed to be deducted for contributions.
Yes, a person under 18 can contribute to a Roth IRA or a traditional IRA as long as they meet earned income requirements and do not exceed income limits. However, you can still contribute to a Roth IRA and make cumulative contributions to a Roth or traditional IRA, regardless of your age. The ability to make non-deductible contributions regardless of income level makes traditional IRAs a valuable retirement savings account that can be converted into a clandestine Roth IRA. Remember that you are also not subject to income limits when you make contributions to a SIMPLE IRA or an SEP IRA; options that are only available if your employer offers them, if you are a small business owner, or if you are self-employed and can open one on your own.