Are there any fonts imitating the correct handwritten forms for Chinese students?
Since the closest thing to handwritten forms for Chinese-language regulation is in the 楷書 (regular script) style, here are my suggestions:


Hong Kong: Free-HK-Kai_4700 https://freehkfonts.opensource.hk/download/ (definitely open source)
ROC (Taiwan): TW-Kai-98 https://data.gov.tw/dataset/5961 (unsure if open source)


The ROC (Taiwan) regular script font (TW-Kai-98) is a government-mandated standard, so you can be sure of its ability to represent the ROC (Taiwan) standard. The Hong Kong one (Free-HK-Kai_4700) is an open-source modification from TW-Kai-98, and they have regulated 4700 characters so far (roughly the total number of characters taught in Hong Kong schools).


  EPSON has made a kyokasho font quite a while back which is free to download, but I haven't checked the license on its use. You can get the link at http://www.wazu.jp/gallery/Fonts_Japanese.html (CTRL+F epkyouka).




As an aside, it is not enough to use the fonts to get the correct character forms for each standard - you need to use the correct input method too. Using a Chinese (Traditional, Taiwan) IME is not appropriate (in an official governmental standard sense) to publish documents adhering to Chinese (Traditional, Hong Kong), or vice-versa, because the suggested characters (Unicode codepoints) that display may be different across the IMEs, although the chance of an actual discrepancy happening is very, very slim.