Assalamualykum.
I asked the same question to an Egyptian sister( MAY ALLAH BLESS HER) and following is what she said:
''wa alikom salam brother,
your questions are in sight, now let's figure them out:
-the sura tauba in fact has many other names, this emphasizes that it is separate, and why without bismillah, it's as u mentioned about the covenant with the infidels as they never make a faithful covenant.
but why in surat lahab, I may say: they 1st sura is an order to Prophet Muhammad, but the 2nd is about informing prophet Muhammad with something.. yet I may add that there's some hadith telling that this man, abu lahab was delighted with the birth of prophet Muhammad and sat free a slave woman for that, so in every Monday he is given some kind of mercy in Hell, I think it was a drink of water as I may remember!
subhanallah!''