I'd also like to replace the yellowish floor tile with grey hexagon or small square mosaic tile that would carry through to the shower (see inspiration photos).

Yes, there will be issues. You need structural alterations to the home in order to do curbless. You also need more room than the topical tub space provides, and your current space doesn't even meet current building codes. And you will need a MUCH bigger budget that to do a simple replacement remodel.

Can you knock out an adjacent wall and teal some apace from another room? What's your budget for the project? 40K? 50K?