Can a convert sit at a corut judging? Why or why not ? Why is a convert not fully jew?

All agree that a convert is 100% Jewish, but just on the particular issue of judging, some of our sages learn from the term written in Dvarim (17, 15) regarding choosing a king "from among your brothers", that it also infers that appointment of judges must also be from those born Jewish. We don't understand the reason behind such Torah commandments, although some suggest that leaders should have the most impeccable lineage possible, in order to command respect. On the other hand, there are many different opinions on this complex issue, all of them cited by R. Eliezer Waldenberg (Tzitz Eliezer vol. 19, ch. 47). Many (including leading authorities like the Rama and Aruch HaShulchan) say that it’s okay if his father was Jewish, which, incidentally is very often the case among (most?) converts today (Shulchan Aruch, Choshen Mishpat 7, 1). The Rashbatz brings that Shmaya and Avtalyon, the heads of the Sanhedrin were converts to Judaism, and accordingly, it was obviously allowed. On the other hand, the Rambam says that it is prohibited, but some explain that Shmaya and Avtalyon were the greatest scholars available, in which case it is (!) allowed. Many (e.g. the Knesset HaGedola, Aruch HaShulchan, etc.) say that if the parties involved accept him as a dayan (which is usually the case), than there’s no problem, but the Nodah B’Yehuda, disagrees. On the other hand, the Tumim (80, 1) posits that it’s enough that the local leaders appoint and accept him (even if most of the community objects!). In summary, if you are asking for a particular convert who wishes to be a dayan, you can tell him that if he invests sufficient time and effort into his learning, there are more than enough places and situations where he can serve as a dayan on a Beit Din! With Love of Israel! Rav Ari Shvat