Create a false ceiling using XPS board instead of gypsum board

You can find the answer to your question in the installation instructions for the engineered floor that you are going to use, and if there isn't data there, call up the manufacturer and ask.

My guess is that it will not be allowed; the XPS is likely to deform easily, which leads that portion of the floor to be unsupported. Flexing of the floor at the seams is a bad thing.

Dow, a manufacturer of XPS products, on their India web site, does not recommend using XPS under a roof deck. This is due to the possibility of condensation occurring between the insulation and the structure.

As far as painting goes, US codes require a 15 minute thermal barrier over an interior foam, in the event of fire. This could be satisfied by gypsum wallboard, obviating the need to paint. For noninsulation interior uses, Dow permits latex paint.

Instead, they recommend using an "inverted roof" where the panels are placed OVER the waterproofing and covered with a ballast material that will weigh the panel down and protect it from sunlight.