1. The most obvious difference/advantage to most people is cost. Its free! The more hidden advantage is that some of the 'free' DBMSs out there are open source. It can be a question of dealing with vendors versus having knowledgeable people working on an open system. Each company has to evaluate its needs and determine what it wants. Each database can have different advantages over another. Some might be faster with SELECTS/UPDATES or dealing with Blobs. If a company has specific needs it might need to pick a DBMS based on that.
2. There are ongoing service/licensing contracts that some companies have that can cost quite a bit (for small companies especially). The main cost in having a DBMS is staff (as with most things). For our company, the only cost for our DBMS are the two machines that it runs on (prod, dev) and me.
3. There is nothing we have that would be a direct representation of data in the db. There are paper reports and stuff that happen normally and that data gets entered. If you mean backing up the db onto paper in a direct manner, then that is not very useful.
4. Postgresql 8.1.9. It is a nice and very easy to use DBMS. It has a nice community and stable developers behind it. And of course it cost nothing for the company, although donations can be made. (and I encourage this for companies that use it.) There is also support out there for it if ever needed. It is amazingly documented too.
5. Well, we are about 1 year into creating a new application for this company. So we are implementing for the first time. What I would say for this is... have users more involved. They expect things to just happen and it is odd. DB reworking can be bad as time goes by, but a good design pays off.
6. I would say no. That would be bad. There are applications like ACT out there or as others mentioned MS Access. It cost and level of understanding is simply to high for most small business to really have a full DBMS. There is a balance act that companies must do as they grow. There is a point where they start building a 'data bureaucracy' which DBs/applications could help with. Each has to decide the benefit of paying knowledgeable staff to deal with this versus how much they need it and can afford. I would say for most that vendor software is the best option for awhile.
7. I have only really worked with relational. Although I have not done research, I believe object oriented DBMSs are still in their infancy. (I could be completely wrong on this) I believe relational systems are well established and have a proven record of their benefit. You could look into the history of some of the major DBMSs for insight into this.
8. I have no delt with Oracle really. I'll take a rational guess. I would imagine it is less configurable. Probably stripped down somewhat to allow people to use them to experiment with or for personal projects. Its good for businesses to get their products out there for free so people can decide if they want to commit. Someone else may know if there is a free commercial oracle system available to businesses?
9. This depends on the DBMS in how much you can do. You could go as far as putting certain data on different sections of a disk to speed up the access times for certain data. You could evaluate how tables are used to arrange data differently, create indexes, or write procedures. Many of the systems have query planners I think that allow you to see what is actually going on.
As far as system configuration here is a postgresql example
page that shows what you can change in how the system runs. To my understanding oracle is the most configurable DBMS available.
10. Time. It simply takes a human being to long to search for data in a physical storage system. A DBMS gives you a powerful advantage in that you can query you data in ways that are simply impossible in the physical world without expending enormous amount of human time to gather info. Also there is the storage of data. I can back up years worth of information in a few seconds and keep it secure, but in a paper world you have thousands of pounds of paper. Data is what is important here and a database is what gives the power of dealing with the data instead of a paper bureaucracy. A good DB will also give you
ACID.
Bah.. I read that question backwards

But my answer still applies. The disadvantage to all of this is amount of data vs cost + knowledge. If it is a real small company with little (manageable) data then really a company doesn't need a DB System. Or, they could at least use MS Access or something.
Edit: fixed a spelling error