I get a message which says "OE removed access to the following unsafe attachments"...

I have never had this before, and I am very doubtful that two people whom I know sent me to (expected documents) which were unsafe. Seems very odd.

Do I need to adjust some settings somewhere?

I was expecting a very important document which someone has emailed me ,and now I can't access it.

Thank you so much, that worked. Now, how on earth did that box check itself. I haven't seen it before.

That default behavior is there for a mostly-good reason. Attachments are where a virus or other malevolant code will come in.

I'm not familiar with more recent versions of Outlook, but if you can specify that you don't want attachments automatically opened (that is, you want to deal with them manually) - that would go a long way toward keeping your system safer (provided you excercise some wisdom over which attachments you choose to open).