Исправьте оплошности: He won39;t be able run quickly. I am sure

1). He wont be able to run quickly.

The participle to must go after the fixed phrase before the infinitive.

2). I am sure you will be able to speak Spanish in three months.

The fixed phrase is to be able to. So in the future tense it requires be after will. Three months needs the plural form on the noun.

3). You mustnt say that. Its not polite.

The modal must expresses the strict prohibition to say the impolite words.  

4). You dont need to wash up. Ive already done it.

The negative modal dont need to shows that is it not obligatory to do something, like no need.

5). She had to invite Susans sister to her party, didnt she?

This question requires the tag didnt she, because the main sentence is in the Past Simple. To make the negative form, we use the auxiliary verb did and the participle not.