Does printing from In-design directly makes the colors any better in resolution than exporting to Pdf and then printing?
The short answer is "Not if you make your PDF properly."
It can, but not necessarily. It all depends on how you export your PDF. Each built-in PDf export preset can affect the color depending on how your layout is set up. When exporting, examine the "Compression" and "Output" sections of the export dialog to see whether the images will be subsampled, to what degree, what destination profiles are being converted (if any) and whether or not image destination profiles are being honored.
Also, the PDFx format can mitigate rendering discrepancies that generally arise on the RIP. Look into what PDFx format works best for your workflow.
This depends entirely upon the nature of the data being printed and the actual device used for printing.
For a home/end user inkjet printer with vector content in InDesign... the PDF may be much, much better since Acrobat is a software RIP (Raster Image Processor) and printing the PDF may circumvent the lack of a RIP in the printer itself.
For laser printers, or printers with Postscript Level 3 support, or commercial press houses, it won't make a difference. (Provided any PDF is exported properly for these uses.)