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Could this result in a SE penalty?
Should they be converted to 301 redirects?
Any problems with directing to an internal page?
To be on the safe side, you should use the 301 permanently moved status as this will instruct the robot to list the new page and remove the old page. A 302 will keep the old page and possibly list the new page. The 302 is a temporary redirect, the 301 is a permanent redirect.
No problems redirecting (301) to internal pages.