Does using a third party(non-Apple) MagSafe 45W power adaptor cause power problems with MacBookAir
Yes, you should be worried. Power adapters which have not been Apple certified can be shoddily constructed, have inferior components, and frequently lack safety mechanisms that prevent harm to your device and yourself. This article at Macworld about iPhone chargers shows some of the problems. This forum thread at MacRumors discusses MacBook chargers specifically.

You may save a few dollars getting a non-Apple branded charger, but if it damages your machine, you may just end up spending much more money in the end.