It seems that you have a strong desire for the small person to be able to behave and interact with objects and the environment much like a large person, and that you have a strongly human centered approach.
I think there was a Heinlein story with a subplot where the children as a hobby wanting to have crew for very small space ship got in trouble for genetically engineering small people who ended up not being very bright. These were small enough to be kept in a dollhouse, or small cage. In that case it was intelligence that seemed to be the limiting factor.
From a physics perspective volume and thus the weight goes as the cube – this is the famous reason why ants can't be as big as horses. Since you are going the other way, proportionally to some extent your little person could end up being strong and durable.
Momentum (mass times velocity) needs to be conserved – so the smaller body is more likely to get pushed around if hit or pushed by something. Wind and water forces could be more problematic. If small enough the terminal velocity could be lower and could fall from higher heights. If very small, things like surface tension could be more important. Lighter smaller weapons may not cause as much damage.
The surface area goes as the square. So as the person is smaller, the ratio of the surface area to the volume becomes larger. This means that the amount of heat lost could be larger, and it could be harder to stay warm. That might be one reason why smaller creatures need to eat more and have higher metabolisms. Due to the smaller surface to volume ratio there is probably a trade off between the amount of energy that the little person can store and use. A normal sized person uses about 1400-2000 calories per day resting or moving around. A tiny person would not use as much energy in total, but proportionally would probably use more when resting, and would not have the reserves of a large person.
The ratio of size of relative objects, and the surface roughness of objects is likely to be important. Being light and strong- perhaps climbing is easier, but there might need to be a lot of climbing.
So with some of those kinds of things in mind for your list of questions.
Strange Gait - perhaps - if very small probably can jump proportionally farther, (more body lengths)
Cannot Carry Lightweight Weapons – Probably some relative percentage of body weight 10-15 percent is very reasonable – may be able to carry as a load something the about the size of its body more easily
Blindness Due To Eye Size – photoreceptors are not a problem – can be pretty small – lots of animals with small eyes. Lenses can also be very small. There is some concern with how much light gets collected, but photoreceptors can compensate.
Deafness Due To Ear Size – again not that big a problem – there are lots of way small sound sensors can be made there could be some changes in the frequency range of hearing if you really go to an extreme. There can be some issue with how much sound gets collected by the external ear but detecting vibrations should not be an issue.
Literally Bursting Into Flames Due To Heat – not a big issue unless other small things like paper and leaves are bursting into hear. Temperature regulation due the surface area to volume ratio could be an issue though if hot or cold.
Smaller Than Current World's Shortest Mobile Man - The toddler answer given above is pretty convincing that this is probably not a problem.
Unable To Perform Basic Functions (Eating, Breathing, Drinking, Etc.) – I think lots of small animals are fine with being small.
Strange Proportions – this is harder to figure out- but I think proportional to the head, the ears might be larger, and the eyes might be larger, not sure about nose. Limbs to torso ratio seems like they could be about the same, but might want a larger torso to help store energy.
Mental Side Effects – if true human biology – I think the Toddler brain answer and chimpanzees and other small primates indicate that a brain size about the size of a human fist could be pretty intelligent. If you take some license and look at birds or dogs they have smaller than human sized brains and do pretty well. Small finches can memorize very complex songs, parrots can have big vocabularies, crows use tools. Etc.
To answer your question – for something on earth that evolved from modern humans for whatever reasons – you could probably end up with pretty small people 18 inches to 3 feet talk that could be active and intelligent etc. The might look a little odd- depending on what kind of climate they evolved in to help with the temperature regulation.
To take more license and for a non-human evolution starting point- especially if there was some augmentation and genetic engineering involved. I think you could have small active humanoids in a story that might be as small as 6-12 inches that could be intelligent complex tool users. To make really tiny people – think you get further away from biology and have to throw in some technology to augment the purely biological systems if you want them to be human like.