Some of my site's threads point to pictures on an external website such as photobucket... Is it possible to have these pics imported to my site so they don't get removed in the future and leave a 'gap' on my site?
Copying material from other Web sites is of course pretty simple to do, and you've had a number of suggestions on how it can be done.
You seem to be fishing for the obvious comment so I will give it to you... taking material from other Web sites in general and putting it into your own site without the permission of the Web site owner is normally considered theft by most people.
There are some sites that will allow copying of their content but most seem not to, and you do of course need their permission and you need not to be breaking any of their system rules in whatever you are doing.
As this could be any Website anywhere if you are talking of links members post I do not see how you can work easily within the law whilst copying other peoples material to your own site.
I don't know if you are happy for someone to copy all the material on your site to theirs.. if not though then obviously you should do to others what you'd like done to you.