I have done 10th. Can I take admission for fashion designing Diploma in any college?

Yes, why not. You can take admission in designing fashion.

After class 12th, it is beneficial for getting better placement opportunities.

After your class 10th, you can only do a fashion designing Diploma (basic or advanced Diploma). To build a better career in fashion designing, I would suggest you to complete your class 12th in any field. After your class 12th from a reputed board, go for fashion designing degree. Fashion designing