How to Manage a 90-Day Notice Period When Changing IT Jobs?

Suppose my actual notice period at my current IT company is 90 days, but I inform recruiters that my notice period is 30 days to increase my chances of getting interview calls.

Will mentioning a shorter notice period (like 30 days) result in more calls or opportunities from recruitment agencies?

If I get selected, is it possible to negotiate with my current employer to reduce or adjust the notice period to 30 days?

Are there any options to "buy out" the remaining notice period so that I can join earlier? Please explain how these scenarios usually work in IT companies.