My first thought is that the scratching means feather mites. You can get a spray especially formulated for birds from the pet shop. Follow directions.
Also have a close look at the feet and the cere (nose). If there is the slightest sign of scaling or crusting you bird will have a condition called 'scaley face'. The crusting is caused by a minute mite that lives in those areas. This is also easily remedied with a solution available from the petshop.
You've done the right thing by washing the damage with salty water.
The savlon, however safe, will have made a mess of the feathers.
To hold a budgie so that no injury occurs to the bird or holder, crock the index and middle finger and hold the neck between those and the body in the same hand - firmly but carefully. The index/middle finger can be slightly straightened so the space between the body and head in increased, making it impossible for the bird to bite. You'll soon learn to adjust your grip so that it can't bite you.
Nine years old is a fair age for a budgie that has been badly managed previously.
A well looked after one (mainly fed correctly and exercised) can easily reach 14 or 15.
Hope some of this helps.