Markdown to LaTeX

Not on its own. Pandoc runs without its standalone option, so you get the body of the document: sections, paragraphs, lists, tables and math, with no documentclass line, no preamble and no begin document. Paste it into your own template between begin document and end document, and it will compile with whatever packages your preamble loads.

Yes. Pandoc's Markdown reader understands dollar-delimited math, both inline and display, and its LaTeX writer writes it back out as LaTeX math. This is the one conversion in this family where math is native to both sides rather than being approximated, so formulas come through as formulas.

Images become includegraphics commands carrying the same path your Markdown used, so your preamble needs the graphicx package and the image files need to sit where the path says. Tables are written as LaTeX tables. No image data is read: the tool passes pandoc the text of your Markdown and no other file.

Pandoc escapes the characters LaTeX treats specially, such as percent, ampersand, underscore, hash and dollar, when they appear as ordinary text in your Markdown. What it cannot fix is missing packages: if your text needs Unicode symbols your engine has no font for, that is a preamble problem, not a conversion problem.

Use LaTeX to Markdown. Do not expect a clean round trip, because your preamble, custom macros and package options have no Markdown equivalent and are dropped on the way back. The file name here is your Markdown name with the .tex extension.