Purchasing sd card will solve "insufficient memory storage" issue? After unsuccesfully rooting my android 4.1.1 tab,I can't download anny apps even though I still have 4 gb of 
free memory on my internal storage.

I've done factory resetting but it didn work,will inserting an sd card possibly resolve my concern?

Can I restore apps I lost by doing this?
Buying a new SD card will not solve the problem. In Android phones, all applications are installed in internal memory. Some apps/games which ask for big data to be downloaded from the net also save the data in internal memory. So, if you insert external memory card in your device, then still you face same problem.

To solve this, first you need a external SD card; at least 8GB more would be better. Then, you need to configure your device so that it forcibly installs all data on external SD card. For more information, read this.