Are they able to like charge my phone bill by simply getting me to key whatever PIN they send to my number?
Yes. They will interact with your mobile carrier and the carrier will send you a text to which you need to either reply or get a PIN from it and input it in the webpage. Obviously this is mostly used for scams but given that most mobile carriers themselves are scammers and make money from this there's no way they'd disable it.
Is it safe to give your number?
Well if your carrier implemented their system right there should be no way to charge someone simply using their mobile number. There should be some kind of extra authentication like texting a link or a PIN. Beware of "WAP billing" though, where the carrier may relax or bypass authentication if you open their authentication page from the mobile connection itself (they detect it based on the origin IP), and as a result simply clicking a link may be enough to subscribe you to a scam.
But assuming the billing side of things is safe, giving them your number may open the door to SMS spam or using your number as a caller ID while spamming others. I've seem it happen in France, where spammers would spoof legitimate mobile numbers for their spam calls and texts.