When I take up a short position, I borrow stocks from my broker and sell them on the market. Does the broker charge interest for this? Also to do this, do I need a 'normal' account or a margin account?
The broker will charge borrowing fees and sometimes a charge called "hard-to-borrow fee".
Other than that you will earn interest on the cash you get from selling the stocks, but you will have to pay dividends. This is because someone else (the party you sold the stocks off to) will now get the dividends and the party who lent you the stocks will miss out on these, that's why you have to remunerate them.
The type of account you need is entirely up to your broker (and besides, it depends on what a 'normal' account for you is, you should at least mention your country or your broker).
Exact rules may be different depending on the size of the investor, the specific broker, and the country.
For both the US and Canada, short sales occur only through one's margin account. And shares that are borrowed for shorting only come from a margin account. Shares held in a cash account are not available for shorting.
From Wikipedia Short (finance) -
The speculator instructs the broker to sell the shares and the proceeds are credited to his broker's account at the firm upon which the firm can earn interest. Generally, the short seller does not earn interest on the short proceeds and cannot use or encumber the proceeds for another transaction.
As with many questions, I'd suggest you contact your broker for the exact details governing your account.