Is the imamate valid for a son who is 18 years old, despite a lisp in pronouncing the letter “ra,” and is he considered to have a speech impediment?

If you are not sure that your son changes the characteristic of a letter and substitutes it, then the default assumption is that he pronounces it correctly, and you should not stop praying behind him. If he has a slight lisp (lathgha) that does not affect the characteristic of the letter, then it does no harm. The Shafi'is have explicitly stated that a slight lisp which does not prevent the basic articulation point of the letter does not affect the prayer, and the rules of the Hanafis do not reject this ruling.

There is no dislike (makrooh) in your son leading you in Tarawih prayers and other prayers. As for the imamate of a stutterer (al-alkan) (one who substitutes one letter for another due to inability), there is a difference of opinion regarding it. The Malikis, some Hanafis, Al-Muzani from the Shafi'is, and Ibn al-Banna from the Hanbalis permitted it, while those who permitted it differed on whether it is disliked. However, the majority view is that his imamate is not permissible except for one like him, and this is what we issue fatwas on. Nevertheless, a layperson may follow whoever he trusts.