1.
Because you are using jugar to refer to a noun, you want to use 'a' to connect the verb and noun. Since 'el baloncesto' is a masculine noun, you will combine 'a + el' to make 'al'.
Enrique le gusta jugar al baloncesto.
2.
This question concerns the conjugation of jugar.
'Mi hermano' is a third-person subject, so you will use the conjugation of jugar for third-person present tense, which is juega.
Mi hermano juega con los niños de su escuela.
