Is it safest to double check my new bitcoin address never showed up in the Ledger (the blockchain) before?
would it be safest to double check

Yes but the difference in safety, although not exactly zero, is approximately zero.

is it true that when there is a collision of address, both that person's private key and mine can move this bitcoin amount to else where

Yes.
Statistically that will not happen in any timespan you or I can properly comprehend. See related topics in right hand margin of this web-page. Especially Is a bitcoin address collision possible if generating 90 million addresses every 4 hours?