Thank you for the description and the images!
Your message describes two problems:
1.) Missing Accent Characters
As shown in your screen captures, some Thai and some Burmese text items does not contain all accent characters.
This problem was already solved in Embedded Wizard >= V6.60. I assume you are using an older version of Embedded Wizard - this is why some accent characters are missing. The problem occurred only, when the Windows font engine detects strange glyph metrics.
Please update to the latest version of Embedded Wizard.
2.) Cut character at the end of a text in combination with an accent character
As shown in your screen captures, the Burmese text items are cut at the end.
This problem is solved now and will be provided in Embedded Wizard V7.10, which will be released these days.
Please update to the new version of Embedded Wizard.
Here is a sample how it appears in Embedded Wizard V7.10:

Concerning your questions:
In case you are using a Platform Package with prerendered fonts (compressed bitmap glyphs), then the Windows font engine is used. In case you are using a Platform Package with an external True-Type font engine, then it is in most cases the FreeType font engine.
The ICU layout engine is not used - this is too heavy (several MB) and not suitable for embedded systems. We have implemented our own layout engine.