MacBook Air Charger 45w vs 65w

Using a lower powered AC adapter than the one that shipped with your Mac shouldn't cause the issue you're experiencing.

Typically the only side effect to using the lower wattage adapter will be the inability to boot your Mac if it's battery is dead, since the lower wattage adapter doesn't provide enough power to power on the Mac without supplemental battery power.

The grey/white loading screen could be either a software issue or hardware issue. To test this you can try the following.

• Power on your Mac while holding option, you should eventually reach a screen that shows any bootable volumes connected to the Mac as well as a wireless network drop down box. If you see your hard drive listed here you can select it and click return to boot to it.
• If your Mac still hangs at the white screen you can try holding the left shift key while powering it on, holding shiftuntil you reach the Apple logo with the spinning gear beneath it. This should trigger safe boot, which runs a disk check during the boot process and disables third party extensions. You may notice limited functionality when/if the Mac boots in Safe mode, see Apple's "What is Safe Boot" article for more info.
• If both of these fail then you can try to boot to your recovery disk, assuming you have Lion (10.7) or Mountain Lion (10.8), and attempt to repair your Macintosh HD boot volume using Disk Utility. To do so you will power on your Mac while holding option, just as in my first suggestion, but instead choose the Recovery volume if it's available. Once booted to the Recovery disk you will choose Disk Utility, select your boot volume (Macintosh HD?) on the left and click "Repair Disk". Once the repair is finished you can try rebooting. If it fails let us know the error reported and we can offer further advice.

If all of the above fail and/or your hard drive doesn't show up in Disk Utility or as an option when booting with option held down then you are likely experiencing a hardware failure.

Hopefully that gives you a good starting point and/or resolution!

Since the Temperature is a major factor in Battery life degradation, slower charging is preferred.

However, if you are charging while consuming /(using your computer) the charger might not provide enough to actually charge the battery and it will get depleted.

In that case using the lower power charging is only recommended when computer is off.

Source 1:

Source 2: