"A further disadvantage is that parents with small families do not have enough children to provide for their needs at an old age..."

[hardyweineberg]

A further disadvantage is that parents with small families do not have enough children to provide for their needs at an old age.
Source: me

1) Is it right to use the preposition "with"?

"Although it may seem as though one or two children can effectively carry out that task, it is not possible, because parents usually develop many health, as well as financial, problems when old."
Source: me

2) I reduced "when they are old" to "when old". Is it grammatical to do so?

 

[Tarheel]

Say:

to provide for them when they are old.

1. Yes.
2. I would prefer "when they reach an advanced age" or "when they get old".