Explain why the expression dudo que takes the subjunctive while no dudo que does not.

... because by using the subjunctive tense ('dudo que'...), you indicate your uncertainty about something.

Explanation:

Example:

Dudo que entiendas lo que estoy diciendo.

corras is the only one that is informal but doesn't follow the suffix rule. correr is the verb. corre is the formal verb form. corra would be used as the formal is corre ended with an a.

your best bet would be corras, it's the only one that is informal but is still wrong