[Doitsu]

IMHO, you're focusing on the wrong tool. Mobipocket Creator hasn't been updated in years and is hopelessly outdated. For example, it cannot create .ncx files, which are needed for Kindle chapter navigation.
Also if you select the wrong display font, Mobipocket Creator might not display characters that the Kindle actually supports.

I just did a quick test and had no problems generating both .prc and .mobi files with the Unicode characters U+2713 and U+2113 in them that were correctly displayed both by Mobipocket Reader and the Kindle app.
(I created the .prc file by double-clicking the .opf file and the .mobi file by opening the .opf file with Kindle Previewer.)

Therefore the Unicode checkmark problems that you're having are almost certainly caused by codepage issues.
If you want to use Mobipocket Creator, you'll need to use utf-8 source files with a byte-order-mark (BOM). (Kindle Previewer can handle utf-8 source files with or without BOMs correctly.)