scale (long response)
I can see a scale insect clearly in pictures 3-4 and 5-6; they certainly are responsible for the sticky residues on the leaves.
Scale are unfortunately, really hard to control. Most of the types of scale that infest house plants have become resistant to many insecticides used in greenhouses.
If one tries to remove the adults physically with rubbing alcohol, or scraping, they will reappear from eggs.
Low temperatures such as 45 deg. (7deg. C) will not harm them. Dwarf Scheffs can take temperatures around freezing, but I don't recommend it, and that still wouldn't get rid of the scale. Most greenhouse scale eggs can survive temps well below freezing.
Soap will wash off the sticky residues, but the hard shell of the scale will protect them from the soap. Still, you may want to wash the plant first before other treatment.
I would disagree; Dawn is very powerful detergent (not soap) and it burns a great number of plants. I would suggest you seek out an insecticidal soap (Safer's, or some other brand) and only use that on plants. These types of soap are made to remove the insect's body defenses with minimal damage to the plant's defenses. I really like Safer's brand and always use it to wash my plants.
However, soaps do not stop the scale. The most effective routes to control scale insects are systemics, and oils.
A systemic is put into the soil and the plant takes it up into it's leaves and stems. This is the most simple and positive way to control scale and mealybug in my experience. Bayer makes the following two products worth considering:
http://www.sears.com/shc/s/p_10153_12605_SPM214684926P?prdNo=12
http://www.sears.com/shc/s/p_10153_12605_SPM214686074P?prdNo=16&blockNo=41&blockType=G41
They contain the active ingredient imidocloprid, which is the same thing in Advantage for cats and dogs. Its very safe for people and pets. These products are approved for use on food crops people will eat.
One either pushes the pills into the soil, or waters the liquid into the soil, like a fertilizer. It might require two or more treatments, but then the plants are protected from insects for a long time, as much as a year.
It is a new product, and so for the most part, the greenhouse pests like scale and mealybug have not developed resistance to it.
Of course, these are not natural, or organic. There are oils that can be used that are natural, but they are less effective and leave a residue of their own on the foliage.
The most well-know is neem, which is pressed from the seeds of a tropical tree. It would be sprayed over the whole plant and works by suffocating the insects, even inside their shell. Here's one example ( and no, I don't work for Sears, I just had their site open).
http://www.sears.com/shc/s/p_10153_12605_SPM214685934P?prdNo=1&blockNo=1&blockType=G1
There are many brands to choose from; most are 70% neem. Its better to buy a neem concentrate over the ready-to-spray versions, so you can choose a stronger solution. The eggs of the scale will survive and so one will need to spray many times at regular intervals (at least once a week) for at least two months.
Neem is very safe for people and pets and only rarely harms plants; Dwarf Scheffs tolerate it well.
Other oils can work too. One brand that is popular is trade named Organicide. Its a mix of fish and sesame oil.
Several brands of mixed food oils are available in the U.S. that all contain clove or cinnamon oil; these are very effective on insects, but in my experience, are really too likely to burn plants.
In non-natural oils there are many choices too. Parafinic oils, Ultrafine oils, light horticultural oils, all could control the scale.
Also, be aware that ants can pick up and move scale to plants. One may need to control ants as well, if they are present.
Ultimately, the OP will have to decide if its more cost effective to treat the affected plant, or replace it.
*shrugs*
