Even if there is no chancre, syphilis can be spread through sexual secretions, and oral sex is always a risk. So, ry not to have any sexual activities until the infection disappears.
Probably not, but if you've had sex with him in the past 3 months (and not just 2 days prior to your sore appearing), you should let him know because he could be your source.
Also, are you 100% certain that your sore appeared the day it did, or did you just notice it that day? I don't mean to sound insulting, but sometimes the sore appears on the underside of the penis, and people don't notice it right away. I don't know where your sore is (and don't even need to know), but if there is a possibility that your sore appeared earlier than you think, you should tell your partner so he can get treated.
And yes, no sex until the sore is gone.