Welcome to the STD forum.
The reason for leaving all threads available for all to read, and the reson for the important information in the Disclaimer message at the top of the forum (which I suspect you did not read) is that at least 90% of the questions asked on the forum have been answered previously. By looking at previous responses, readers can find the answers they need without spending the posting fee. In this case, much of what you asked was answered only a few hours ago, in another question this same day. Please take a look:
http://www.medhelp.org/posts/show/1228025
To your specific questions:
1) Intermittent burning may or may not be significant. It is conceivable you acquired nongonococcal urethritis (NGU), but probably not, since there is no discharge. If the symptom persists a couple more days, see a health care provider, such as your local health department STD clinic. But my guess is that the feeling is emotional/psychological, not evidence of an infection. If it goes away, don't worry about it.
2) A bite mark doesn't increase the STD risk.
3) The STD risk is low enough from oral sex that testing usually is unnecessary in the absence of symptoms. But you can always do it if you want the extra insurance. Again, your local public health clinic or your primary care provider can arrange for testing for common infections.
4) There is no risk for HIV, no point in testing. (But HIV testing is often done automatically when other STD tests are done, so your clinic or doctor might recommend it.)
5,6) They call them STDs because they cannot be transmitted other than sexually. There is no risk of household spread or of transmission to your kids. Here is a thread that explains STD transmission in great detail. Start reading with the follow-up comments that begin December 14:
http://www.medhelp.org/posts/show/1119533
As for the safety of sex with your wife, I cannot give you any guarantees. But if I were in your situation, with the knowledge I have, I would continue unpotected sex with my wife without fear of infecting her.
Bottom line: Oral sex is safe sex, with little STD risk. But if your urinary discomfort persists, see a health care provider. But feel free to see a clinic or doctor for testing if this reassurance doesn't settle your fears.
Regards-- HHH, MD