Electrical Problem?

The following behaviors have been occurringg for the past 4 weeks now.

• A "Key fob not detected" message sporadically appears in message console while driving even though the key fob is laying on the dash.
• Any action which uses the horn. The sound suddenly changed one day, it's not nearly as loud and sounds muffled.I estimate the volume has dropped by more than half.
• There are sporadic key fob failures to.
o lock/unlock doors
o open lift gate
o remote start
• Will occasionally get a check engine light. DTC code is "Engine running too lean"
• Ultimately, the battery died last week and car was completely unresponsive. Had to get a jump to get it started
• The strangest thing that has started occurring is an electronic "sizzling sound" coming from the top side of the engine when switching the ignition to "On" or "Run" but not starting the engine (does not occur when in accessory mode. At least not audible)

Bottom-line.I took it to a Jeep dealership, and they diagnosed it had a defective battery and replaced it. Said this should solve all the other issues but it hasn't. The issues above are continuing to occur.