Question

And is quadrilateral. is AB+BC+CD+DA>AC+BD?

Answer 1

YES
In triangle ABC by the triangle inequality we have AB + BC > AC.
In triangle ADC by the triangle inequality we have AD + CD > AC.
In triangle BCD by the triangle inequality we have BC + CD > BD.
In triangle BAD by the triangle inequality we have AB + AD > BD.

Add these up

(AB + BC) + (AD + CD) + (BC + CD) + (AB + AD) > AC + AC + BD + BD
2AB + 2BC + 2AD + 2CD > 2AC + 2BD
2(AB + BC + AD + CD) > 2(AC + BD)
2(perimeter) > 2(sum of diagonals)