2.9 understand that the current in a series circuit depends on the applied voltage and the number and nature of other components

The current in a series circuit is the same through out all parts of the circuit. It is worked out using the equation I= V/R. So its the total of the voltages received by the components divided by the total of all the components resistances.

2.8 explain why a series or parallel circuit is more appropriate for particular applications, including domestic lighting

In a series circuit everything is connected on one line. This means that the voltage is shared out between every component: this makes it useful for supplying low power things like fairy lights.

In a parallel circuit different components are connected separately to the supply. This means that of one component breaks the others can continue being powered as the whole circuit is still functioning, this makes it practical to use. It is also good for charging higher power things as the potential difference is equal all over a parallel circuit so each component receives the full voltage.

2.7 understand the difference between mains electricity being alternating current (a.c.) and direct current (d.c.) being supplied by a cell or battery

Direct current flows in one direction only. It is supplied by cells and batteries. It comes out as a straight line on an oscilloscope.

Alternating current changes from one direction to another rapidly. Mains electricity is alternating (interestingly this is because the electricity has to go through transformers on the national grid which only work on ac current, although that's not relevant here!)

2.6 use the relationship between energy transferred, current, voltage and time

energy transferred = current × voltage × time

E = I × V × t

n.b this is the same thing as saying power x time

2.5 know and use the relationship: power = current × voltage

power = current × voltage

P = I × V

2.4 understand that a current in a resistor results in the electrical transfer of energy and an increase in temperature, and how this can be used in a variety of domestic contexts

As a resistor slows down the movement of electrons, the kinetic energy that was moving them is converted into heat energy. This can be used, for example, in hair dryers or heaters.

2.3 understand the uses of insulation, double insulation, earthing, fuses and circuit breakers in a range of domestic appliances

Insulation is covering a live wire with a material that won't conduct the electricity.
Double insulation is a precaution that makes sure the live wire cannot touch the casing (so no shock can be conducted) usually by putting extra insulation round that wire. Double insulation can also mean that the casing of an object is plastic so even if the wire touches it, it wont conduct.
An earth wire is touching the case so that if a current is in the case, it will be directed through the earth wire, this will then take the current to the earth. Additionally the surge of electricity in the wire may break the fuse.
Fuses are sections of wire in the circuit that melt if too high a current goes through them. They come with different maximum currents.
Circuit breakers have an electromagnet that is activated if the current goes above a certain limit. the electromagnet pulls an iron switch towards it, this opens the switch and breaks the circuit.