If your incoming messages are skipping your Inbox and ending up in Trash, the cause can be misconfigured filter, or a setting on your Forwarding and POP/IMAP tab.
Please make sure you haven’t created any filters with the actions Skip the Inbox (Archive it) and Delete it that would affect the messages in question (You can check them under Settings > Filters). If you have many filters or have complicated filters in place, you may need to edit the Skip the Inbox (Archive it) and Delete itaction to guarantee that they are not at fault.
If you’ve enabled forwarding in your account, please ensure that you have not selected delete Gmail’s copy in your forwarding options.
If you’re using a POP client to access Gmail, please ensure that you have not selected delete Gmail’s copy in step 2 of your POP download options.
For your problems in sending mails to others, check if using the following interactive troubleshooter helps.
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