On to the first picture, which prominently features the "eye spots":
Side view of a fifth instar Manduca sexta.
Before I talk about the "eye spots", I'll introduce a little bit of insect respiratory physiology. Insects deliver oxygen to their cells using tracheae, air-filled tubes that travel throughout their bodies. These tracheae branch into smaller tracheoles, which travel near virtually every cell of the insect's body. While insects do have a respiratory pigment (hemocyanin, in contrast to vertebrates' hemoglobin), most of an insect cell's oxygen demand is supplied by air diffusing directly from the outside atmosphere through the tracheal system to the cell, and thus insect hemolymph (blood) plays little role in oxygen delivery.
The "eye spots" are actually M. sexta's spiracles, the openings to their tracheal system. These spiracles can be opened and closed, and it is hypothesized that this gating mechanism evolved to reduce water loss. Each spiracle connects to a single large trachea, which then branches out and supplies oxygen to the nearby tissue. The trachea between segments are often interconnected by longitudinal tracheae, so if one spiracle doesn't open, oxygen can still be delivered to the tissue.
Since insects have a respiratory system that is connected directly to the outside air through spiracles, their mouths play no role in respiration, and insects have no functional equivalent of lungs or gills.
A fifth instar Manduca sexta feeding on tomato leaf.
The white circle around each spiracle marks its edge. The spiracles in these pictures are closed; you are seeing the pigmented spiracular cover, not the inside of the tracheal system. Manduca open their spiracles only rarely; I watched a M. sexta's spiracles under a microscope for about 15 minutes on Friday, but didn't see a single spiracle open. They're able to open their spiracles so rarely because they have a very low metabolic rate, and thus consume relatively little oxygen (they're ectotherms; endotherms, like humans, have on average a metabolic rate seven times greater than ectotherms of a similar mass).
The spiracles do indeed appear as though they are intended to look like eye spots. I haven't seen any papers on this (ed.: And how many Manduca papers have you read in the past year? That's right, pal: zero), but it does seem likely that they're using them to make predators think twice before attacking. The caterpillar may be attempting to make its terminal segment appear as though it is its head, luring predators into mistakenly attack its hind end first, which would allow the caterpillar a chance to fight back (now now, don't laugh).
Prashant also brought up another good question: do related species of Manduca have the same spiracular cover designs? There are a number of species in the genus Manduca besides M. sexta, including M. quinquemaculata (larval picture), M. albiplaga, M. florestan (larval picture), M. jasminearum (larval picture), M. muscosa (larval picture), M. occulta (larval picture, enlarge the image to see a spiracle near the head), and M. rustica (larval picture). For a more complete list look here (scroll down to the genus Manduca).
All of the species above share the same black-in-white spiracle design, though the species vary in the prominence of their spiracles, and it appears that M. sexta is the only species in this list with yellow coloring on its spiracles. However, with only a few pictures available for each species' larva, it's hard to come to solid conclusions. I know that M. sexta's coloration depends somewhat on the diet it is fed (e.g. this picture of a caterpillar reared on artificial diet), and it is relatively easy to find pictures of M. sexta larvae where the spiracles are somewhat differently colored.
As a side note, M. quinquemaculata, besides having the coolest epithet ever (it rolls off the tongue so beautifully), is the actual tomato hornworm; M. sexta is more properly called the tobacco hornworm.
Incidentally, insect blood is greenish, not red, because it lacks hemoglobin (the red oxygen-carrying compound in vertebrate blood); instead it contains hemocyanin, which is copper-based and thus blue-green when oxidized.