Can’t run one particular program from Terminal without using its full path

I think the problem is that you are not specifying the p option.

From the manual for patch:

For example, supposing the file name  in  the  patch file was

  /u/howard/src/blurfl/blurfl.c

setting -p0 gives the entire file name unmodified, -p1 gives

  u/howard/src/blurfl/blurfl.c

without the leading slash, -p4 gives

  blurfl/blurfl.c

and  not  specifying  -p  at  all just gives you

  blurfl.c.

Whatever you end up with is looked for either in the current directory,
or the directory specified by the -d option.

So the command should be something like:

patch -p0 <custom.patch

or you could specify the directory to which the patch should be applied:

patch -d /path/to/dir <custom.patch

Your prompt is messed up, specifically PS1:

PS1=$[\033]0;37m]

that's missing a lot of escape characters (\e[) needed for the colors (and most useful parameters for a PS1). That's also why you get the 37m in the terminal window title. Try setting it to something different by running:

export PS1="\e[0;31m[\h:\W \u]\$\e[m "

and see if that works. It should give a red (thats \e[0;31m) prompt showing hostname (\h), current working directory (\W) and logged in user (\u) inside brackets [] and the bash exit status of the previous command (\$). Note that at the end the color is reset to the default of the session with \e[m .

If the above worked, you only have to find out from which configuration file your "bad" PS1 comes from: look for an "export PS1=" line in ~/.profile, ~/.bash_profile, ~/.bashrc, (as M K already suggested in his answer) and put in the above version.

There are a lot of answers around here with helpful colors codes and inputs for configuring the PS1, like this one for example.