Depends on what the outlets are controlling, size of the wire, and size of the breaker.
Depends on the size wire used in the circuit. If you wired the circuit with AWG #12 wire on a 20 amp breaker then you can install no more than 12 outlets. If you wired it with AWG #14 wire on a 15 amp breaker then install no more than 9 outlets. This is assuming only outlets are on the circuit and nothing else.
Two 20 Amp circuits with the outlets staggered so a different circuit is on two adjacent outlets. Should be GFCI protected.
Your home electrical wall outlets current capacity is governed by the breaker that feeds that circuit. In most home situations the wall receptacles are fed with a 15 amp breaker. Dedicated outlets could have a higher ampacity as they are installed for specific appliances or devices. To check your circuit, plug a lamp into the outlet. Start flipping the breakers off. When the lamp goes out that is the breaker for that circuit. Look on the handle of the breaker and it will tell you the capacity of that particular circuit.
The breaker panel. Breakers are placed in series with all outlets.
Somewhere you have a loose or broken connection.
Don't mess with an electric panel if you are not absolutely sure what you are doing. To add a circuit you need a breaker, wire sized to the new breaker and the outlets, lights or devices that are powered by the new circuit. If you have spare slots in the panel you need to get the proper breaker for the panel and just knock out the panel cover for the new breaker. If there is no space in the panel, you may be able to find a dual breaker that just takes up one space in the panel and substitute for an existing breaker.
No. The breaker must protect the circuit components such as wiring, outlets and switches that are connected to the breaker. Therefore if you have a 30 amp circuit as dictated by its components you need to protect it with a 30 amp or less breaker.
It would be quite unusual to have a single 60 amp circuit with outlets and lights. You would have to use very heavy wire to each light and outlet. Typical lighting circuits would be protected by 15 amp breaker and a circuit with general purpose receptacles would have a 20 amp breaker. A typical lighting circuit might have 10 to 12 fixtures and receptacle circuit might have 8 outlets. If you don't know how to size a circuit get an electrician.
For the 120 volt outlets on the wall use a 20 amp breaker wired with AWG #12 wire. The circuit must be GFCI protected. Any 240 volt outlets must be wired according to what they will be powering.
Your question is a bit vague, but let's try a two part answer. If you have a GFCI breaker in an electric panel you should only have one connection at the breaker, but the breaker will protect all devices on the circuit. If you are talking about a GFCI outlet, they are equipped to extend the GFCI protection to other non-GFCI outlets by using the proper "output" connection on the GFCI.