All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We have already clarified in our answer to your question number 2718534 that this prayer place in your town does not take the ruling of a mosque because it is a rented place, as you have mentioned, and it is not endowed to be a mosque.
Therefore, you are not obliged to go to pray in this place even if the Imam does not pray quickly.
Hence, there is no harm if you pray in congregation in your house with your family, and you will get the reward of praying in congregation, and you will attain the reward of praying with the congregation, Allah willing.
If the Imam in your mosque prays so quickly that he does not observe the pillar of Tuma’neenah (submissiveness), or does not recite the the Faatihah properly, then the prayer behind him is not valid.
If it is true that his recitation of the Faatihah is faster than his Tasleem, then he might not be reciting it completely.
Moreover, Tuma’neenah is a pillar in prayer without which the prayer is void. The criterion for Tuma’neenah, as stated by the scholars, is that each body part settles in its place (before one moves from one position to another). So, the minimum time is that the parts of the body should settle, because it is pausing between two movements.
It was also said: it is to the extent of saying the obligatory mention of Allah (which saying Subhaana Rabbiyal 'Atheem once).
Therefore, if the imam moves from one pillar of the prayer to the other without allowing his body parts to settle (properly at their place), then his prayer is not valid, so do not pray behind him.
For more benefit on the Tuma’neenah, please refer to Fataawa 180233, 200531, 326782, and 338716.
Allah knows best.