I am slowly learning how to do SEO for my website and in the process changed a few URLs. Now, some of them are already visible in Yahoo answers and I am unable to update them to the new URLs. I can do 301 redirects for these URLs in YA. However, what about the old URLs that show up on Google Search? Should I do 301 redirects for them as well? And what about urls that I have deleted once and for all. I am getting 500 error for them in Google Webmaster Tools. How should I handle those errors? Should I put in a remove URL request for the URLs that give the 500 errors?
Holy cow! I an not sure I followed all of that. So let me explain some things starting with the 500 error.
The 550 error is an error that needs to be fixed. The 500 error represents a real problem. I cannot tell you what that problem is since I have no idea about your site and so forth.
Here it is from Wikipedia: 500 Internal Server Error - A generic error message, given when an unexpected condition was encountered and no more specific message is suitable.
You need to look in your web server log files and see what accesses are giving you the 500 error and fix them.
As for 301 redirects. Generally, they are only used when a the page has moved or been replaced. Sometimes they are used to give a user another option. Note each URL and create a 301 redirect in your .htaccess file for each. Here is an example, though there are several ways of doing a redirect. This is just one.
Redirect 301 /articles/how-to-back-a-cake.html http://www.domain.com/baking-techniques.html