When teething is it normal for toddlers to want to bite people / things very hard, and sometimes till slight gum bleeding? Is the slight bleeding a big concern?

Yes, teething time they will want to bite on anything they can grab hold when they are at baby stage. How old is your toddler? Bleeding gums is normal as the gum tissue is very tender. If bleeding is a lot, then you may need to visit the dentist to check whether it is an inflammation.