Battery-Fan-AC-Engine jerk

[msnathan]

Hello, Can someone please share their thoughts on the following issues being faced with my Peugeot 307 Hdi manual car. Car History: Year: 2005, Meter:140,000 Kms, purchased 10 months ago, carried out 1 major and 1 minor service since purchase
1. Fan keeps running after engine is turned off and it runs until battery runs flat. when trying to restart, have to use a battery jump start to power up.
2.Recently started to notice vehicle jerk big time, but usually when I turn on the Air conditioning system
3. This problem happens randomly: when I try to change the temperature settings and/or change fan speed on the climate control panel, no physical change is noticed. Example, when trying to achieve heating from lower set point, heating does not take effect. And when fan speed is increased, not much air is being directed from the grills (But I could hear the air pressure inside the grill)

Please can you share your similar experience and any solution to fix these issues - Many Thanks