No, don’t start Shabbos according to R’ Tam’s zman. Start 18 minutes before sunset like everyone else.
As for ending Shabbos, do it whatever time you want.
As for Mincha, you should daven before sunset.
Zmanim for tzeis can be tricky. They are not the same all over the world. In Israel, for example, tzeis comes very quickly after shkia. R’ Tam’s zman was based on where he lived, in France.
R’ Moshe Feinstin zt”l once decided to see when tzeis should be in the Eastern US. He determined that it is 50 minutes after shkia. I keep Shabbos until that zman, as it is the most accurate for our area.