It is in the oblique case because there is an implicit postposition between पढ़ने and जाती, corresponding to the preposition 'to' in the English sentence. In the oblique case, पढ़ना becomes पढ़ने.

The postposition is necessary (though not expressed) because जाना is an intransitive verb and cannot take a direct object.

Note: 'पढ़ना' with the 'ढ़' is the verb 'to read/study'. 'पड़ना' with a 'ड़' is the verb 'to lie'.

No. It's the simple present tense.

The past tense would be जूलिया हर दिन पढ़ने जाती थी - Julia used to go to study every day.