My internal CD drive has stopped working. If I buy an external drive as a replacement, will this work if I have to use boot discs in the future? Will the PC automatically try to locate the disc in the internal drive or can I adapt it to look to the external drive? Will I have to have the internal drive repaired to be sure that I can use boot discs in the future if my PC fails?

It IS possible to boot from a USB source, so nothing to worry about.
Mind you a replacement internal driver can be very cheap..

OEM manufacturers like HP Gateway and Dell, do not always make it easy for you to get inside and do things yourself, but it can be done. Aside from figuring out how to get the old one out and the new in, you have to consider form factor. Most drives these days are short and will fit in most cases but there are a few longer ones that might not fit. The upside is you can upgrade from a CD drive to a DVD burner and have much more functionality. If your nervous about going inside, find a place that will install what you buy for a fee. Big Box and Mom and Pop stores charge more for the same things you can buy on line, so being able to do it yourself saves bigtime. Be adventurous.