Gst on sale to sez

Dear Sir,

I am a works contractor. If I supply goods & service to a SEZ client without charging any GST :

1) Who will apply for LUT, Client or me?

2) Can I purchase the said materials (which supplied to SEZ client) without GST?

3) If I purchase the said materials (which supplied to SEZ client) with GST, can I get the Input credit of the GST against the sales invoices made to other claints?

Regards

Santanu