1) I have been trying to get projects but yet I have succeeded in getting only one small project. Is there any mistake I am making ?
2) Is it good to join an agency to work ? Is it safe ?
3) Can I still work independently while working with agency? Would I require connects to join agency projects?
It may take a while to win a job, especially in competitive categories, and submitting proposals doesn't always guarantee that you will get hired or a chance to be interviewed, but you shouldn't give up on sending proposals to potential clients.
You may want to check the following articles to help you improve your profile and have a higher chance of getting noticed by clients: