This should answer all your questions:
You can have more than 10 Secret Bases,you can have all the Secret Bases in Hoenn filled up(exept for your's),the registering thing you do in your friend base is so if you want to keep that base and you are mixing record's with a friend,that Secret Base won't get deleted.
Here is an Example,I have Emerald and Ruby now:there is a Secret Base(not your's)in Emerald in the part of the Safari Zone you know the tree that's to the right,now you are facing that tree and in Emerald the Right spot of that tree is in use now you enter that Secret Base and Register it.
Now here is Ruby:
The same spot that is in use in Emerald,you have that Secret Base spot in your Ruby in use(not you,your friends),now in Ruby go to that Secret Base and Register it.
Now here's the mixing records part:
Note that everyrthing in () explains the process of Mixing Records.
You can only have Registered 10 bases in both Emerald and Ruby(Note that when mixing records the bases that you didn't register will get exchanged when mixing records,here an Example:Emerald Secret bases(not the registered ones) and Ruby's Secret bases will get exchanged,Emerald's Secret bases will be exchanged to Ruby while Emerald aquire's Ruby's Secret Bases,exept the registered ones)
Now go back to the field and check that the 10 Registered Secret Bases weren't gone,now the other unregistered Secret Bases were exchanged so you get new Secret Bases.