I just purchased a used Tamron 45mm lens, and its rear element is a bit dirty. Am I allowed to clean the rear element using microfiber and lens cleaning solution + lens cleaning tissue?
You can absolutely clean the rear element as you've discussed - it's done exactly the same as the front element is cleaned.
Caution must be used because if, for example, a piece of grit were on the rear element when you used your cloth, and you damaged the element's coating, the damage is far more likely to affect your image quality than it would be if you did the same damage on the front element. The rear element is very close to the film/sensor plane and the image is nearly in focus at this point, whereas the front element is far from the capture plane and far from the point of image focus, so a surprising amount of dirt or damage can be on a front element with minimal effects on image quality (except if you are shooting into strong light, like the sun, when the issues will tend to cause flare).
Blow off any particles or gently brush them off, using a blower brush, then use a microfibre cloth, or a piece of lens cleaning tissue moistened with lens cleaning solution, to clean the element. The standard advice is to clean from the centre out to the periphery/edge.
You can absolutely clean a rear element on a lens, much as you'd clean the front element. Exercise the same caution and you'll be fine.
The only danger with a microfiber cloth is that it should be grit-free (you may inadvertently scratch an element because whatever you got off a lens the last time might still be in the cloth), which is why some folks use cleaning solution and cleaning tissues or Zeiss single-use wetwipes (I get mine at Walmart for both my camera lenses and my glasses).
Another common tool you can use is the Lenspen, which uses a dry carbon compound to clean the lens (but this may leave small carbon particles behind, so be sure to use a blower or brush afterwards). Lenspens can also be used for sensor cleaning.
If you really want to go to town on cleaning your lens, you could read about the methods used by lensrentals.com for their high-volume turnover of lens cleaning. But it's serious overkill for most photographers.
Use a rocket blower on it first to remove debris, make sure the rear element isn't recessed into the lens body (it definitely shouldn't be with a prime), and polish gently with a lens cloth or lens pen. If you use cleaner, spray it on the cloth first and don't use much.