It sounds like you're using an exchange (thanks to your pop-up comment), so there is no catch-all answer, but generally, if an exchange assigns you a receiving address, that will be associated with your account permanently. Some exchanges gives you the option of requesting a new one, and may even assign you a new one for each transaction, but it should generally be safe to keep reusing it to receive coins.
If you're using an online wallet, yes, it's the same every time.
No. They will need your address's private key to take control of it. You yourself may not even have access to said private key as it depends on the exchange/online wallet.
You don't need to keep it secret. There are no risks, except that everyone can see all of your transactions. There is a slight risk on reusing addresses, but it mostly has to do with quantum computing, which isn't here yet. It's all privacy concerns otherwise.
I strongly suggest you do not start out with an online wallet, as they're generally less safe than desktop and hardware wallets. If you decide to buy Bitcoins, consider using a lightweight desktop wallet like Electrum (www.electrum.org), and transfer your coins there.
Also, don't be afraid to ask questions. It's much better than losing money thanks to a rookie mistake.