does my fiat punto elx 2001 have a alarm and a immobiliser ?

immobilisor yes
its in a sealed chip sealed into key
no alarm unless retro fitted

on the key there is hole where the logo should have be will there still be a immobiliser chip

swerve said:

on the key there is hole where the logo should have be will there still be a immobiliser chip

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its buried in the key
i had the unfortunate luck to have to disect a key earlier this year and broke the glass ferule holding the chip because the key casing was hard and brittle because it was so cold at work

look here via atom man
https://www.fiatforum.com/punto-mk2-2b-guides/331723-swap-immobiliser-transponder-old-key-new.html

Without pics, difficult to be sure, but the chip is usually embedded right in the plastic bit of the key..

Best guess, if it's an original FIAT key, and the car starts, no code light, it's in there.