Alert height is only used for fail safe (Cat III) approaches. On the B777 any loss of redundancy above the alert height you may have to go-around if the failed equipment is required for the approach. You may also revert to a Cat IIIa approach from a Cat IIIb provided the wx and equipment allow.
Any further losses of redundancy below alert height will be inhibited (includes EICAS messages except for 4 specific ones) The approach can be then continued.
The TAC is designed not to give rudder inputs following an engine severe damage, or when inputs to the TAC are invalid. Turing the TAC off then back to AUTO may re-engage it.
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