How do I download non market apps on my android smartphone?

Somewhere in the settings for your phone there might be a checkbox where you can tell your phone it can download apps from non-market sources. If you enable that then if you can find an app someplace besides Google Play, you can download it.

Unfortunately, I dont think doing that will help you. You have an old phone with an old version of Android. If you're already having problems with many of the apps you CAN download, there's no reason to expect things to get better once you're able to download even more of them.

I hate to say it but the only way to really fix this is to get a newer phone, not go nuts trying to download apps from different places.

Unfortunately your phone android version is too low
You should search "apps for android version. 1.5"
It is jot advised to download and install from market or even internet
As your phone maybe too weak to run those android apps
But still you can try
It may slow or hang your phone
Just give it a try
There will be no virus