Prayer

If you managed to pray one Rakah before the sun started to rise, the prayer was done on time.

If one does not know Arabic, s/he can make general dua’a in their mother tongue in sujood or before Salam. It does not break salah.

You can offer night prayers or any nafl prayers whenever you want providing it is not a time of prohibition

No, it is not Mandatory.

If you managed to pray at least one Rakah before the time of Athan of Asr, then you have prayed it on time. You would be sinful if you had delayed it for no legitimate reason.

It is still valid.

If you and him were in the position of ruku at the same time, this is a valid Rakah even if you didn’t recite the Fatiha.

No, as you seem to be an OCD patient. You have to ignore such thoughts and wiswas.

You must not do this as a habit. Try to offer the prayer earlier. However, if you prayed one Rakah before the sun began to rise, your prayer is valid.

Of course it must touch the prayer mat.