Few very good tips in that video - a good reminder for all of us.

Some good tips except for the avocado one. The pip should not be left in.

Just lay the cut avocado on a flat plate with the pulp side down and cover the whole lot tightly with cling wrap and store in fridge.

I've always found the best way of keeping lemons and limes fresh is to wrap each one, individually, in aluminium foil, and keep in the salad drawer of your refrigerator.  They will last for several weeks.