I have recently had issues with different electrical appliances ...
Having the outlets very low down must put a strain on the leads where they enter the plug. Other than that any suspected problems with the electrical supply need to be discussed with the supplier.
/ light bulb ...
Incandescent bulbs tend to fail when there is problems with the supply voltage (i.e. surges) - that is something your electricity supply should be able to help with. Another cause is if the lamp housing/fixture gets too hot.
However, nowadays you should be using CFL or LED lamps. LEDs in particular need adequate airflow to keep them cool - many older bathroom light fittings don't allow for this as they are designed to keep out steamy humid air (and fingers)
/ bathroom wiring packing up.
That sounds very alarming. Ideally there shouldn't be much wiring in a bathroom. A light, maybe an electric shower and a towel rail, maybe a shaver outlet. Given the age and quality of what is visible in photos, I'd consult an electrician.
a sizzle and spark often happens when taking the plugs in and out.
That shouldn't happen if you turn off the switch at the outlet first.
Sparking tends to erode contacts and cause further sparking. The outlets might need replacing (I'd get them moved higher up the wall, with wiring suitably protected in a channel chased into the plaster).
do I need to change the switch box?
As AndyT commented - you might not strictly need to but many people would want that old-style fusebox replaced by a modern consumer unit with RCD protection (or RCBOs to make later fault-finding easier)