J&J hasn't been approved yet in the UK. The alternatives would be Moderna + Pfizer. Also, I doubt you'll get a choice of alternative, just whatever one is available in your local area at the time.
https://www.businessinsider.com/millions-johnson-and-johnson...
It means that the watch dogs are watching.
With that said we don't know if other problems will be discovered in the long run, but that's what regulators are there for. In the case of AZ vaccine, they're clearly working as well.
So yeah, it's working even if people have died with a direct cause of a vaccine.
Also we've already heard since then that the US has put J&J in charge of the factory to only produce their vaccine.