Can any broker like TD, TradeKing, Schwab, etc, can charge me just because I have entered my details and open an account in their website?
Even if I didn't deposit anything?
Yes. A broker can charge you for opening an account, if you agree to this. Make sure you check what you are agreeing to, when opening your account.
Many brokerages will only charge you a per-transaction fee. In some cases, even that fee may be waived. I buy my mutual funds through TD Waterhouse (in Canada), for example, and pay no fees because of my other accounts with TD Bank, and because I buy TD Waterhouse mutual funds.
If I did not have a market value of $25,000 or more with TD Waterhouse, though, I would be subject to an annual administration fee of $25 for a Basic RRSP account (in which I can buy stocks and mutual funds). See http://www.tdwaterhouse.ca/document/PDF/apply/forms/tdw-apply-forms-521778-pdf.pdf, page 7. I am not sure if that would be assessed immediately upon opening the account, or at the end of the first year.
It seems to me you should be aware of fees and how/why they are incurred. If a broker says they charge, say, $10/qtr maintenance fee, and you are under the waiver balance, you'll see that fee applied to the account, even if you've not yet funded it.
Why open an account with no assets? In my case, I had funds that would be transferred from a retirement plan to a new IRA. The IRA was opened with no balance so it could receive the funds a week later. But, I had a family balance that waived fees.