Absolutely! There are STDs that are transferred through bodily fluids (though not really saliva) and there are STDs that are spread through skin on skin contact.
The fluid based STDs such as HIV can be passed through open cuts, shared needles, etc. but they have never been proven to transmit through kissing or saliva.
The skin based STDs such as herpes and HPV can be passed through heavy petting and genital contact even without intercourse.
Can an STD be passed through oral sex? Yes, not the fluid based STDs, but the skin based. You can get HSV1 or 2 from oral sex. HSV1 is usually oral (cold sores) but it is commonly transferred to the genitals. HSV2 is usually genital, but can sometimes be transferred to the mouth.
HSV2 on the genitals is the most likely to cause an outbreak followed by HSV1 orally. HSV1 on the genitals causes outbreaks but not as bad, and HSV2 in the mouth rarely causes more than one outbreak (if that.)
It is incredibly rare to catch an STD from a toilet seat. The bacteria dies very quickly after it leaves the body, so you don't have to worry about that!
experience, researching herpes