There is a possibility of being bitten, as there is when playing with most any wild animal.I have a dog that goes a lot places with me a people always ask before petting him: "does he bite" my simple response to the question is: " He doesn't Bit
ME" That being said, it is not very common. And for the most part biting is not a typical behavior for most species of octo. Some are more prone to biting, like
O.rubescens. When I'm playing/petting mine I make sure to be very conscious of where my hand is and where the octopuses beak is. I make sure not to allow and untrusted octopus to crawl all the way onto my hand where my flesh is within reach of the beak. I just keep rotating and lifting my hand straight up out of the water to keep the octo at bay. A feeding stick works well to move arms that are getting to close for comfort in the early stages of contact.
The tugging you are describing is very typical. both D and myself have found its best not to pull back but to just stand your ground. hold your hand still, dont let him pull you towards hium, but also dont pull your hand away. eventually the octo will stop trying to pull and begin to investigate more. the biggest thing is to take your time with them dont rush it. be prepared to just hold your hand in the tank for at least five minutes to as long as 20 minutes while the octo just dances around investigating.
Another tip is to play with your octo on one corner and always that corner then feed the octo in the other corner. This helps seperate play time and feeding time.