I'm new to the biking community, I was wondering if I would be able to change my wheel/tire from 700c to 650c since I am short. How would I go about it, any recommendations for wheel/tires? I have a Retrospec Mantra Single Speed XS 43cm frame with 700c tires.
If this is your bike then no. It has rim brakes, and they won't line up properly if you try to install smaller wheels.
You say that you are short; the only thing that smaller wheels will change is the standover height (height of the top tube). All the rest of the bike's geometry will be the same, including distance to the cranks and distance to the handlebars. It might actually cause problems because smaller wheels will put your bottom bracket closer to the road, increasing the chance of a pedal strike. (Unless you also change your cranks.)
Perhaps you simply need to buy a smaller bike?
I hope people don't mind if I don't directly answer the question as posed. It's already been correctly pointed out by @DavidW that if you change the wheel size, you will lose the ability to brake.
If the bike had disc brakes, you could downsize to 650B wheels. However, aside from raising the chance of striking your crank as you turn, I believe this would decrease the bike's trail, which would make it less stable in turns. That could be a negative if you weren't expecting it.
Retrospec is not very clear about their bike geometry. They say only that the 43cm Mantra has a level top tube and 30.5" (77.5cm) standover clearance, and that it's designed for riders who are 4'9" to 5'1" (144.8 to 154.9cm) tall. I think the standover clearance is relatively high for that frame size, although I am used to frames with sloping top tubes.
If the only issue is that you have little standover clearance, I would keep riding the bicycle. That assumes that you can get the correct saddle height, that you have the saddle fore-aft position set correctly for you, and that given this, you can reach the handlebars comfortably. I think most road cyclists have to stretch a bit to put a foot down on the ground when sitting on the saddle, so this should not be an issue either (provided your overall saddle height is correct for your leg length!!); at a stop light, you can simply step forward and stand over the top tube, perhaps leaning the bike to the side. Consider that when you are riding the bike, you're not in any danger of hitting your crotch on the top tube because you're sitting in the saddle.
If this were a mountain or cyclocross bike, then because some falling is involved, I would probably counsel differently.
Most bikes have sloped top tubes. This enables them to fit a wider range of people at the same length, i.e. the bike's horizontal dimension, usually measured in reach or top tube length. With level top tubes, people with short legs would have to size down. The recommendation that you have at least an inch of standover clearance probably stems from the days when a) bikes had level top tubes and b) their seat tube length was about equal to their top tube length. So, if you couldn't stand over the bike, there was a decent chance it was actually too long for you also.
Perhaps you are thinking of toe overlap, i.e. your toe strikes the wheel when you turn the handlebars sharply. I can sympathize, as it can be disconcerting for new riders. However, consider that when cycling at speed, you mainly steer the bike by leaning it. So, toe overlap won't cause handling issues at normal traveling speed. It's possible to hit your foot at low speed, but you can adjust to this. In normal riding, you should not crash due to toe overlap.
(As a side note: I have some toe overlap on my cyclocross bike. I have crashed due to this issue, but only once, and it was in a sand pit. Contrary to best practices, I was flailing a bit and I happened to unintentionally steer my wheel sharply just when one foot was at the 9 o'clock position. This should not happen on the road.)
Many short riders benefit from 650c or 650B wheels. At my height of 5'5", it can depend. I prefer 700c wheels due to parts availability. However, the shorter you get from my height, the more the case for a smaller wheel size increases. This is another set of SKUs for the manufacturers, however, so I suspect most mainstream brands don't spec 650c/B wheels on their smallest frames. I believe that mainstream brands like Trek and Specialized do rate their smallest frames for riders around 4'11" and up, with 700c wheels. I can't recall which major brands use 650c/B.
For human interest, Emma Pooley is 5'2" tall, a former professional road cyclist, a former World time trial Champion, and the current holder of the women's Everesting record. She talks about her fit issues with 700c bikes, and the rationale and process behind getting a custom bike with 650c wheels in this article by Anne-Marije Rook for Cyclingtips.
For technical interest, 650c wheels originated in triathlon. Greg Kopecky writes about the history of 650c wheels on Slowtwitch.com. However, it's not a very common standard at the time of writing. As discussed on that article, manufacturers are converging on 650B, which is similar but not identical in size. By my recollection, this standard may have originated in mountain biking.
I think that in the past, some road cycling manufacturers (usually niche ones) may have offered 26" wheels for their smallest sizes. This standard definitely originated in the MTB world, and it is considered obsolete. The availability of rims and tires for road cycling in this size is poor.