Will my fasting – Allah willing – be accepted if I swallowed saliva that is thought to have come from toothpaste after the dawn adhan, even though I rinsed my mouth repeatedly, and do you advise me to use toothpaste after the suhoor?

As long as you rinsed your mouth before the Fajr adhan, this means the effect of the toothpaste has been removed from your mouth, and your fast is valid. Do not open the door to obsessive doubts for yourself. If using toothpaste will open this door for you, we advise you to stop using it.