1. Why it stops working
From the pictures on
O-Gs wiki and from my experience, it looks like the board has a voltage comparator circuit with output which allows to cut off the cells from terminals. So no intelligence, just a simple cutoff if cell voltage drops below 3V.
2. Will it starts if connected to charger for days
No. For a very specific voltage it is possible to to have the cells half-cut off I guess, but there's a very small chance you will encounter this situation in practice. It won't get back to life without connecting directly to cells.
3. Should I open it into two halves, breaking the welded plastic
Only if you want to replace cells. If you only want to try resuscitate existing ones, it is better to remove the sticker and find the cell terminals there. You could enlarge the opening below with a modelling knife or soldering iron, if cell terminals are not visible.
4. Why not open into two halves?
You will have to then glue it again, tight enough to make it fit the drone. If you tape it around instead, the tape will eventually break due to sliding in and out of the drone. I mean, you will probably have to tape it anyway, to allow proper glueing.
And if you just go below the sticker instead, your opening stays and you can fix it again later.
5. Should I replace cells
The overdischarged cells will no longer work as good as new ones. How bad it will be depends on how deep the discharge and how long they were discharged. If the cells were at 0.5V or lower, the recharged battery will not allow more that a minute of flight, before either landing or falling down with "Power error" showing in the app.
Also, sometimes cells recharged from such a low voltage start excreting more hydrogen when under high load.
So it might be interesting to recharge in order to see first hand how the li-poly cells work, but it is likely you will have to replace the cells to comfortably use
Tello with the battery.