Can I fill an application for a PhD program, and send the scores of GRE and TOEFL later? How much later?
It depends on the university and the department and there is usually no way to tell from the outside unless the website is explicit. Unless you have information to the contrary, you should treat the deadline as the deadlines for all materials to arrive. 

Many universities/departments will red flag missing TOEFL scores from international students and treat the file as incomplete - which means the application won't even get forwarded to the admissions committee. Some programs will also red flag missing GREs for both domestic and international students. The committee won't see these files. 

In the application management system I used at my old department, I could run an alternate search for incomplete applications and still find incomplete or flagged files, but they wouldn't show in the default view and certainly not in the exported spreadsheet we used for committee ranking assignments. 

So if your materials are arriving late, I'd write to both the graduate school and the admissions committee director or graduate studies director and make sure they know to flag your file for further attention. They may also tell you there's nothing they can do about an application that is missing material. 

By the way, we usually have made our decisions by mid- to late- February so your scores arriving in March will definitely be too late and your application would likely get rejected as incomplete (unless you can argue that the TOEFL is inapplicable because you went to an English speaking college or some other reason).