From my course instructor, he has repeatedly emphasized and asked us not to use the "inline" keyword for functions. He says it is not "portable" across compilers and is not "standard". Considering this, are there any "standard" alternatives that allow for "inline expansion"?
Your course instructor is wrong. It is standard. It's actually in the current standard, right there in section 6.7.4 Function specifiers (C99). The fact that it's a suggestion to the compiler that may be totally ignored does not make it any less standard.
I don't think it was in C89/90 which may be what some embedded compilers use but I would give serious consideration to upgrading in that case.
However, even where inline is available, I generally leave those decisions up to the compiler itself since most modern ones are more than capable of figuring out how best to optimise code (and usually far better than I). The inline keyword, like register and auto, is not something I normally worry about at all.
You can use macros instead since that's relatively simple text substitution that generally happens before the compile phase but you should be aware of the limitations and foibles.
Or you can manually inline code (ie, duplicate it) although I wouldn't suggest this as an option since it may quickly become a maintenance nightmare.
Myself, I would write the code using normal functions without any of those tricks and then introduce them where necessary (and only if you can demonstrate that they're needed, such as a specific performance issue).
You should always assume that the coder who has to maintain your code is a psychopathic killer who knows where you live :-)