The EU kicked Britain out of Horizon ( despite Israel being members ).
No, the UK could not be a full member of Horizon any more as it was not a member state any more and there was no legal basis for it to continue to be a full member of Horizon. The terms of the UK's associate status were agreed in the TCA.
Rejoining Horizon was negotiated a few years ago but the EU decided to hold it up.
There was no timeframe specified in the TCA over Horizon. However the UK did not implement many areas in the WA and TCA concerning Northern Ireland. So you're complaining about the EU taking its sweet time to do something at the same time as the UK was guilty of not keeping its side of the bargain. Oddly enough now the UK has finally promised to keep its side of the bargain the EU has stopped dragging its feet. Funny that.
The government decided to do the right thing and close the schools affected so nobody would die from this.
I suppose it also did the right thing in 2010 as well when the slithy Gove decided to stop renovating the school estate in good time (aka Building Schools for the Future) meaning nobody would have been in danger, no schools would have had to be closed at all, and nobody's education would have had to have been interrupted.