Is it safe to use a debt card which is linked to my checking account with a visa symbol on it on the internet ?
Yes, just use it with store you trust, or only use PayPal with people you don't know.
No. Never use a debit card online Many debit cards do not have the same protections credit cards have so if someone gets your number they can wipe out your bank account and you may never see that money again.
Yes debit cards are very safe. Always be cautious with the stores you use. Like better known stores like Amazon or Target or Best Buy. Use common sense.
to be extra safe, open another checking account in a different bank and use it just for online stuff. that way you only have the amount of money in it you need to spend.