Certainly a typo, Peter means ./
Answer:
You can put the . in your PATH, and define it in the login files; e.g. in .profile have
export PATH=/bin:/usr/bin:/usr/sbin:/sbin:.
For safety reasons the . should be after the standard pathes, so an "ls" will run /bin/ls or /usr/bin/ls, not a ./ls
BTW the answer for 1) is a plain yes.
You might consider creating your own dedicated directory for the script in question (and those that will follow :). Put that directory in your path, not the ".".