name of firm ends with Co. ??

Of Course yes. 

yes

yes it can

defiantely yes

yes, u can do that

yes

Don't misunderstand words co. it doessn't refer to PVT or public co. It is written to denote that thier are more than 1person carrying on same profession or business.Take eg of our CA firms u will notice co. at end.If there is company registered under Co. act 1956 , name usually end with LTD except in sec:25 Co.'s