Masbooq and Laahiq

Looking at the next Musallee to determine how many rakaats one missed

Q: A person arrives late to the masjid and misses a number of rakats with the imam. When the imam says salam, he thus has a number of extra rakaat to make up. But he doesn't remember how many. In order to find out, may he pray slowly and see how many extra rakaats the people around him do, since they joined the prayer at the same time as him?

Masbooq (latecomer) joining the Salaah

Q:

  1. If the Imaam is in ruku, does one have to first tie the hands and stand in order to get the rakaat, or does going directly into ruku after takbeer suffice?
  2. If one makes takbeer and while going into the sitting posture the imaam makes one salaam, can one still join the salaah?
  3. If one has to complete missed rakaats in jamaat: In the final sitting, does one read attahiyat, durood as well as the dua, or just stop after reciting the shahadah?