When should I add "to" before an infinitive in a parallelism sentence?

Solution 1:

All he can do, as it turns out, is to stay by her side, take her to wherever he goes and hope someday she will wake up.

When we have the verb 'do' in the subject, we normally omit 'to'.

Solution 2:

All he can do, as it turns out, is to stay by her side, take her to wherever he goes and hope someday she will wake up.

The above complex structure is a coordinate structure. When it come to the full infinitive or the to- infinitive, it has it rules that it follows together with Conjunctions.

Now, whenever there is a conjunct "and" used after a to- infinitive verb, the second verb does not take the particle.... "to"

 So one could say:

• All that he has to do, is to stay and take her to the hospital.

instead of

• All that he has to do, is to stay and to take her to the hospital. (wrong).

Moreover the sentence, I won’t elaborate on his excellent judge of character or other things like willingness to take responsibility and to trust in his team here, determination and so on is wrong when it comes to the full infinitive clause

it is likewise the same as the former sentence. to take responsibility is to- infinitive or full infinitive, and the second verb need not take a particle "to".

Hence, the correct structure must be:

I won’t elaborate on his excellent judge of character or other things like willingness to take responsibility and trust in his team here, determination and so on.

Research more on Non- finite Clause structures.

Thank you.