Let say I want to know the current flowing through a new line connecting bus A and bus B. I generate a Thevenin equivalent circuit of the system seen from bus A - B.
Sure you can do that. But, power systems consist of a large number of nodes and lines. In such a big framework, using the thevenin's theorem would be very difficult as well as time consuming. That is why load flow is preferred for such computations.
Yes, this valid for the snapshot at which you constructed the static equivalence of the system, but I would not follow that approach unless the system is small. The load flow is then better, and systematic as mentioned by Utkarsh.
Of course you can. For the simple network it is easy, but for the network with several hundreds or thousands of nodes you need to use solution algorithms such as NR or GS or CI method for power flow solution.