Obvious move is to try the bulb(s) before looking for something deeper.

Side and dip would likely be on different fuses anyway, so blown bulbs is the most likely cause. Dual filament bulbs usually blow the dip beam filament first as it gets more use. A blown sidelight bulb often goes unnoticed until the dip beam gives up, unless you specifically check it regularly, so it may well have been gone for a while.

H4 is very likely.

No idea about the sidelight, it'll probably be some sort of 5w bulb. Assuming that there's no clue in the handbook, just pull the old one and take it into the shop with you for comparison.