yes you are supposed to leave the bottom one turned on all the time; the supply is timed so that it is only live during the overnight cheap rate*. Unlesss you empty out all the hot water there should be no need to turn on the high-priced upper element. you can turn the lower element off when you go on holiday.
You can get stiff plastic foam sleeves lagging for pipes, you have probably got some pipes in 15mm size and more in 22mm size, the insulation is available at any DIY shed, or plumbers merchant. Measure about how much you need (get plenty). It has a slit down the side so you can push it round the pipes. You have to open the slit with your thumbnail or a blunt knife but you will see where it is moulded in. You can cut it with a breadknife to mitre the corners, or you can buy ready-made elbow pieces but they are quite expensive. As long as you push it on from the side it will bend round easy bends on the pipes. You may need some strong tape to bind it round bends and joints. It is usually cheaper in packs of 5 x 1metre length. There are two grades available, the thicker British Standard one is better and should be used for pipes in unheated areas (especially lofts and under floors) but if you have room for it, put it on your hot pipes too. It is made of foamed polythene. climaflex is a good brand but there may be an own-brand which (if it feels stiff) will be OK, it will cost in the region of £1 per metre. there used to be cheap soft floppy lagging available which falls apart, but I have not seen it sold recently.
*I have assumed that you have a dual-rate electricity tariff, like Economy 7 or similar. If you don't, and if you have storage heaters as well as the electric cylinder, you probably hould have. If not, I will change my advice.
