Well, you shouldn't and it's highly unlikely that you insert it by accident, because you would have to push really hard.
However, some guy managed to insert a tampon in his urehtra. See here:
With enough effort I'm sure you could force a tampon into your urethra, but needless to say it would hurt like hell and likely lead to a urinary tract infection. If you're asking if it's possible to insert it into your urethra accidentally, no it's not possible as you'd feel it and would have to really force it in your urethra. The urethra is small and sensitive, tampons have no place in the urethra.
No, you urinate from the urethra and a tampon goes into the vagina.Both the vaginal opening and the urethral opening are right next to each other within the vestibule of the vulva, but they are not the same hole and it is not possible to insert a tampon into the urethra. A person can urinate as normal when they are wearing a tampon.
There are many places where one can learn how to insert a tampon. One can learn how to insert a tampon at popular on the web sources such as YouTube and Playtex Sport.
If you already have a tampon inserted and you were to insert another then it may be difficult for you to insert the second tampon. Inserting the second tampon may push the first tampon into your cervix which may result in menstrual cramp type pains. Also of course with two tampons you will be at much greater risk of vaginal infections and toxic shock syndrome.
is there a special way to put a tampon in my anus
No, of course not - a tampon would be inside the vagina, urine comes out via your urethra.
You either insert a tampon or put on a pad
Yes, it's safe to pee while wearing a tampon - a tampon goes into the vagina, where as urine comes out via the urethra. If your tampon has a string then it would need to be moved out of the way to avoid it getting wet.
If you insert the tampon applicator past the grip, you may find it challenging to remove the applicator, but I'm sure you will get it out. There is no great concern.
You move the tampon string out of the way of your urethra, or you can use tampons without strings to avoid the problem all together.
You can try putting the ring in a tampon applicator and insert just as you would a tampon.