After one has finished the tashahhud, and before actually saying salam, they should supplicate with any du’a that they like, as this is one of the times of response.
Ibn Masud narrates: I was once praying, and the Prophet, peace be upon him, Abu Bakr and Umar (were all present). When I sat down (in the final tashahhud), I praised Allah, then sent salams on the Prophet, peace be upon him, then started praying for myself. At this, the Prophet, peace be upon him, said:
“Ask, and you shall be given it! Ask, and you shall be given it!” (Recorded in al-Tirmidhi)
Again, in regards to making du’a within the prayer, it is best to say these in Arabic if know any du’as in Arabic, but if you do not, then it is permissible to ask Allah in your own language until such time as you learn them. Du’as from the Qur’an and the sunnah are particularly recommended for use in the prayer. Outside the prayer you can make any du’a in any language you wish. And Allah knows best.