No, budgies do not hybridize with parrots, as budgies are their own specie and cannot hybridize with lorikeet. my budgies didn't liked my two opaline Brouke's parrots, with two female budgies attacked the 1-year-old male Brouke's parrot, because it was too close to their nest boxes.
I do not know which lorikeets were closest related to budgies.
Both sexes of budgies are seed eaters, and flowers were chewed, not licked.
1% of today's domestic budgies, had genes for red, orange colour, in their DNA.
The yellow colour are trace of their former red colour, and today's wild budgies still have yellow feathers.
You need budgies DNAs, to look for genes for red colour.
Think of resent mutation...spangle budgies.
If were the red budgie were to exist, the breeder will face the problem of choose which of budgies to part with and the red budgie have to be bred with mother or father to produce more red budgies, then young red budgies will be part with unrelated budgies. Healthy budgies are capable of procreat at 200-230 days old, after completion of post-juvenile moult, with male budgies mating while outermost primaries 10th are either juvenile or growing.