Regarding ITC

yes.You can claim Input,provided in invoice they should mention their and yours GST numbers

yes we have given GSTIN NUMBER TO THEM and they have coted GSTIN in that invoice

What is the effective date of Registration..?

effective date of registration is 30/12/2017

you have to file your december gstr 1 and gstr 3b
conditions
1- in date 30/12/2017 and 31/12/2017 if you have any sale or purchase in these date you have to file 3b and gstr 1 with invoices which raise in these date
2- if in these date ( 30 dec and 31dec ) no invoice then file your nill 3b and gstr 1for december

if you selected quaterly then you have to file(3b,gstr1) december individual and your quater starts from january ....

Thanku very much