Greetings.

A plain young single apple tree not supposed to self pollinate; receives in some branches, a few grafts from cuttings of other apple varieties which are good candidates for fruiting.   

Will it work for pollinating the single tree itself instead of need for a compatible orchard around ?  Would it also happen among/between the grafted branches ?  Is that called 'cross-pollination' ?   Is there a preferred season for grafting ?  March ?

Yes, a single tree can become self-pollinating with grafted branches. It's something of a fad among nurseries now to graft four or five different kinds of fruit into a single tree.  It should be done when the tree is quite young - 2-4 years is recommended. In late winter or early spring, when severe cold is over, but the leaves are not yet open.  

Edited October 30, 20232 yr by Peterkin