Relays: understanding "Rated carry current" and "Maximum contact current"
You seem to be mixing up the ratings on the coils and on the switching contacts. Notice the ratings you quoted come from two different tables in the datasheet:


If your power supply is being used to drive the coils, then you need to consider the required coil current to switch the relay. As your item #1 says, a 10 A supply could potentially supply 100 100-mA coils simultaneously.

If your power supply is being used to drive the load (switched by the relay) then you need to worry about what current your load draws when powered by 12 V. If it does indeed draw 3A, then you could only power 3 such loads with a 10 A supply.

If one relay is being used to switch current to the coils of a bunch of other relays, then you get the limit of your item #2. The 3 A allowed through the contact of the first relay is enough to power the coils of 30 100-mA coils that are its load.

Also, if you want your system to be reliable for a long time, you'd probably want to de-rate all of these specs rather than operate the power supply or the relays at their maximum current limits. (The coils will operate at roughly the spec'ed currents due to the coil resistance and Ohm's Law)