How to make sure the clipping in a .svg created with Inkscape are imported well in Illustrator

I received a .svg design made with Inkscape and I need to convert it to .ai to send it to a printer. But when opened with Illustrator, lots of features were changed.
Most notably, some of the masks (“clipping” as Inkscape calls them) are not taken into account, (objects that should be cropped were suddenly not) although strangely some of the objects were cropped properly.
I also spotted a few issues with the texts, too, but this is easily fixed.

How to keep the text in vector in Photoshop without rasterizing it or flattening the layers when exporting to PDF?

After many tests in all kind of PDF presets, I couldn’t figure out how to keep the text layers as vector and still have the quality of InDesign without using it. Everything I tried was rasterizing the texts. It seems like PDF/x rasterizes the layers too.