Can it also translate as "May Aamir..."?
Yes. The Hindi sentence can be talking about either ability or permission depending on the context.
So why isn't it जाना?
Same reason it is 'can go' and not 'can to go' in English. सकना functions as an auxiliary and is attached to the root form of the main verb, not the infinitive.
Shouldn't their be a को or से after Delhi?
The को is omitted with the verbs आना and जाना.
If you're talking about coming/going from Delhi, you need to include से.
Ticket book kara do