Can Cookie's Be Set Manually To Bypass Security

I have put an Access database inside an access_db folder on Godaddy and written some .asp pages that query it. I am trying to make sure that I take necessary precautions against hackers reading or even writing to the database. Maybe someone can give some remarks about whether any of these concerns are realistic, and if so, why and what I could do about it?

1) Could someone somehow navigate directly to the database and read or write to it (the access_db folder seems to have no read/write permissions as set by default by Godaddy, but how secure is that?)

2) I permit entry through use of a a userid and password that are looked up in an mdb in the same folder (not listed in the html itself). If there’s a match, I store the userid as a session cookie. Then, to visit any other pages, each page first checks to see if the cookie is empty before proceeding. Is it possible for someone to set the cookie themselves and thus break through (can a cookie be set manually?) If so, would it help if I mandated that the cookie be set to something specific (right now it just has to be non-blank) or can they find out what the cookie should be set to as well?