> Is it safe to update to 188.8.131.52?
Safe as in not loosing your books? I didn't loose mine when I upgraded.
Safe as in not bricking your KT? Read the pinned post about Kubrick. It's a live disk that can unbrick your kindle - or even take it back to 5.1.2 after the upgrade.
> Will the jailbreak still be working?
You'll need to reapply jailbreak, dev-certs, jbpatch as a minimum. Read the first post in the pinned KUAL Unified Application Launcher thread. There you can find an archive of pre-requisites. The pre-requisites for KUAL are the same for jbpatch, I believe.
> Can I use jbpatch again?
Be aware that jbpatch for 184.108.40.206 has fewer features than 5.1.2 -