cc-mode + compilation

[David Trallero]

I would appreciate if there is a way in which I could compile my "C"
project (just execute a make) without care about the directory or file I
am editing. For example, if my project is in ~/my_projects/prjA/ and I
am editing /tmp/foo.txt, I would like to make something like: M-x
(re)compile-prj and execute a simple make.

I tried M-x compile and then to write as command: cd ~/my_projects/prjA
; make, but seems emacs is not always able to locate correctly the error
and warning messages (this is something I tried time ago and I do not
remember in which cases it did not work fine).

Is there also any emacs-package that use speed-bar to present the
"project" files (I assume there must be an interface to add and delete
files from the "project")?

Thanks a lot,
David