I'm going to be honest with you, transferring between systems is not an easy process and you are going to have to do a considerable amount of editing and bug testing. Be prepared for the endeavor, because "starting over" from scratch with a fresh installation will look better the more you look into your project.
That being said, I've been there... I just converted from a version of eAthena that was 8 years old... NIGHTMARE TERRITORY. So, I want to offer my help and expertise in the matter.
First, I have some questions. I'm assuming you have complete control of your VPS? Root access, blah blah blah. And it's running on a linux server, you said? How many years old is this server?
Now, your questions:
1) You don't have to wipe your databases, but you'll have to update them by adding new columns to many tables and editing certain fields... Manually, to make sure everything works with rAthena. If you have a bajillion players this becomes a much more difficult task.
Most of the tables have different values in rAthena and some have different compositions of what is in those values. Main differences are item_db fields in RE mechanics and the mob_db is missing an entire column, but otherwise the database fields are mostly interchangable. Your big task is migrating save data on the MySQL database.
2) As michaelsoftman said, you don't have to update your version of the MySQL software... Just updating the tables (big charts that store the data in lists). If you don't care about your characters saves just delete everything and start fresh.
3) I suggest you learn about editing your MySQL tables and understanding their function before attemping anythng here. You're going to be looking at those tables a lot if you're planning on migrating data.
4) michaelsoftman's got this one. You can use all existing mob sprites for whatever purpose, but just be ready to modify their stats so your pre-re characters don't buy the farm.
Do you have any custom databases or custom mods? If you don't, this means you can use a fresh rAthena install and just migrate your data to rAthena compatible MySQL tables. However, the next step is getting a client that works... This is important and often way more difficult than it sounds. You need to compile the rAthena source code to fit the right RagRE client date or make sure you are using a client exe compatible with a pre-compiled rAthena release.
What client version are your players using?
I hope I gave you information you needed and helped get you started. Feel free to ask more. =P