At stock clocks with a stock fan, I don't think you need to worry too much about temps.
Prime95 is a stress test, so in reality, you will probably never stress the CPU that much in day to day operations.
As for the heatsink moving, it's probably because of the TIMM (thermal paste). Mine does too.
Don't overtighten the heatsink. You will probably bend/crack the motherboard and/or cause damage to CPU socket pins.
If you wanted to,
1. Reapply TIMM using high quality product-Artic MX-4.
2. Get an aftermarket cooler-Hyper 212 (as mentioned), CNPS10X Performa offer good value. If doing so, try not to use bundled TIMM.
3. Install extra case fans for better airflow.