How to deal with embeded color profiles? Export with embeded or not?

I Know it may not be specific Corel Draw x6 question but wasn't sure where to look for the answer.

I really struggle to understand the color profiles. I do understand what they are but I am very confused what should I do with client's files when they have some profiles included and if I should tick the ISO profile box when exporting from corel draw to print.

I DON'T CARE HOW IT LOOKS ON THE SCREEN - the print result matters.

My questions are:

1) If you export file as PDF for printing purposes (large format digital printers) is there any reason for using embeded ISO profile?

2) What function it has since CMYK break down should be the main information the printer gets to mangage colours using its own profiles depending on how the particular inks represent CMYK value.

3) I fell into trap a couple of times when people sent a PDF with embeded profile which changed the CMYK break down of the artwork that was originally printed in the past. How can I tell looking at the PDF to be carefull and can expect 'surprises' ?

4) We print some menu covers for one company that needs to match colours to samples very often so to provide colour referece and avoid colour matching every time I printed big colour chart from our HP printer as they look printed on that printer (with its profile and inks). I thought that this way I solved the problem but someone just sent PDF from Corel Draw with colour profile embeded and previously we printed the file straight from PDF and now  someone saved the same pdf as EPS from Adobe Acrobat. As default when saving as EPS file Acrobat I think preserves originally embeded profile and as a result two prints - one from EPS and one from PDF have different shade. I don't know what to do to avoid these situations in future and whe best practice would be.

THanks if you can help!