i)As you move across a period the number of protons in the nucleus, and so the overall nuclear charge, increases. All extra electrons are roughly the same energy and distance from the nucleus. This means there is little extra shielding effect or extra distance to lessen the effect of the increasingly positive nuclear charge. This means that as you move across the period, the attraction between the outermost electrons and the nucleus tends to increase. This means a larger first ionisation energy is required to remove an electron as you move further right across the periodic table.
ii) Aluminium (Drop at groups 2 and 3) - Mg : 1s22s23s2, Al : 1s22s23s23p1. The extra electron in Al is added to a 3p orbital. This has very slightly higher energy than 3s so on average is a greater distance from the nucleus. It also has a small amount of shielding provided by the 3s2 electrons. These factors combine to break the trend and give Al a lower ionisation energy than Mg.
Sulfur (Drop at groups 5 and 6) - P : 1s22s23s23p3, S : 1s22s23s23p4. Both atoms show identical shielding as the electron is being removed from the same 3p orbital. However, the 3p orbital contains 3 suborbitals, and each are filled one electron at a time. In P the electron is being removed from a singly occupied suborbital. In S however, the 4th electron is found in a suborbital which already had one electron. The repulsion between these two electrons makes it easier to remove, and so has a very slightly lower first ionisation energy.