You can use a 3 wire feeder to supply a separate building, if...
- The installation was in compliance with a previous edition of National Electrical Code (existing premises wiring).
- An equipment grounding conductor is not run with the supply to the structure.
- There are no continuous metallic paths bonded to the grounding system in each structure (bonded water, or gas piping, other conduit, etc.).
- Ground-fault protection of equipment has not been installed on the supply side of the feeders.
National Electrical Code 2014
Article 250 Grounding and Bonding
II. System Grounding
250.32 Buildings or Structures Supplied by a Feeder(s)
or Branch Circuit(s).
(B) Grounded Systems.
(1) Supplied by a Feeder or Branch Circuit. An equipment
grounding conductor as described in 250.118 shall be
run with the supply conductors and be connected to the
building or structure disconnecting means and to the
grounding electrode(s). The equipment grounding conductor
shall be used for grounding or bonding of equipment,
structures, or frames required to be grounded or bonded.
The equipment grounding conductor shall be sized in accordance
with 250.122. Any installed grounded conductor
shall not be connected to the equipment grounding conductor
or to the grounding electrode(s).
Exception No 1: For installations made in compliance
with previous editions of this Code that permitted such connection,
the grounded conductor run with the supply to the
building or structure shall be permitted to serve as the
ground-fault return path if all of the following requirements
continue to be met:
(1) An equipment grounding conductor is not run with the
supply to the building or structure.
(2) There are no continuous metallic paths bonded to the
grounding system in each building or structure involved.
(3) Ground-fault protection of equipment has not been installed
on the supply side of the feeder(s).
If the grounded conductor is used for grounding in accordance
with the provision of this exception, the size of the
grounded conductor shall not be smaller than the larger of
either of the following:
(1) That required by 220.61
(2) That required by 250.122
Changing from a 30A breaker to a 50A breaker can only be done, if you also change the wires to 6 AWG. In which case you'll have to follow current codes, and install 6/3 with ground. Breakers (and fuses) are always sized to protect the wire connected to them, so you can't change the breaker size without also changing the wire size (unless you're going down e.g. 50A to 30A).
However, depending on what you're doing, you may not have to change the breaker at all. If the planned circuits in the structure are not going to be fully loaded, you may well be able to supply the subpanel with a 30A breaker. Just because the subpanel has 50 amperes worth of overcurrent protection, does not mean the supply breaker has to be 50A. Whether or not you actually need a 50A breaker on the supply, depends entirely on what the subpanel will be powering.
Best Answer
...And you didn't put a concrete-encased conductor (UFER ground) in the slab? Sigh. That's the easy way out and the most effective ground you can make in most places.
Yes, you need a grounding electrode (ground rod) local to the detached building. Connecting to reinforcing steel in the slab would have provided a very good grounding electrode, but if it's already poured, that ship has sailed.
6 AWG solid is the default minimum size for a connector to a grounding electrode. 8 AWG might be acceptable given that the feed size is 10 AWG, but I'm having trouble tracking down the exact language where that is mentioned. It's one of the messier (or more confusing) sections of the code (IMHO.)