Is it necessary to press the feet together during prayer?

Your question has two possibilities:

1. A man pressing his foot against his companion's foot in the prayer line: This is a desirable act, based on the hadith of Nu'man ibn Bashir: "I saw a man pressing his shoulder against his companion's shoulder and his ankle against his ankle." 2. A worshipper pressing his foot against his other foot: This is disliked. He should keep them slightly apart, neither bringing them too close nor moving them too far apart.