Is it permissible for someone praying the regular Sunnah of Dhuhr to pray four rak'ahs with one taslim, and what should be recited in the first tashahhud, and should a surah be recited after Al-Fatiha? And what should be the intention of someone who prayed alone and then saw a congregation and prayed with them?

For someone performing four non-obligatory rak'ahs, such as the Sunnah prayers accompanying Dhuhr, they may perform them separately with two taslims, which is preferable. They may also perform them connectedly with one taslim. If they perform them connectedly, they may suffice with one tashahhud in the last rak'ah, or they may perform tashahhud after every two, three, or four rak'ahs. As for reciting a Surah after Al-Fatihah: if they pray with one tashahhud, they should recite a Surah in all rak'ahs. If they pray with two tashahhuds or more, they should recite it in the rak'ahs preceding the first tashahhud.