Yes & no. Certain head/neck cancers (oropharynx, tonsil, tongue) are associated with hpv infections in ~40% cases; typically in young non-smokers & non-drinkers and also young women. These cancers respond better to standard treatments. Oral sex is a risk for hpv infection in the oral areas but typically an std refers to infections such as gonorrhea, chlamydia, herpes, etc.
Possibly. Interesting question hpv is now becoming an increasing risk for head and neck cancer. Most people are exposed to it but only a small percentage develop oropharyngeal cancer. That is why it is recommended to give young boys the vaccine. It is in some way an std yes. Unclear if oral sex is the cause !