1. She was very slow at the beginning, but she didn't give up.

(What is the opposite of 'at the beginning'? Is it 'at the end, in the end or by the end'?)

2. Wilma tried very hard to be able to walk again.

(What is the function of 'to be able to walk again'? Is it the object of 'tried' or 'an adverbial phrase' modifing 'tried'?)

1. Yes, either "at the end" or "by the end" is the opposite.

2. It looks like an infinitive phrase acting in the position of a direct object after "tried."