you are welcome BigDave in this forum and I would like to tell you that this is a PUBLIC FORUM, so it is for everybody ! Anybody can sign up and The Staff of TalkAboutIslam.com encourages everybody to sign up, Muslims and non-Muslims too.
As for your questions here are the answers:
1. Which is correct: Islamic or Muslim? Or are they interchangeable?
we say "I am muslim" and "he is non-muslim"
and we say "this is an islamic subject"
I hope I am clear enough, I think examples would be better to clarify the meanings of those two words, don't you think so?
2. Is (are) there a proper greeting for Holidays, such as Ramadan? Or. as I am not a member of the faith, should I not mention this?
Sure my friend there are too many greetings for all occasions, please visit our
Beautiful greeting cards section :hearts2
3. Are there any holidays that have gift giving involved (I just really like giving gifts 
)
LOL, yes me too I like gift giving, who doesn't !!! BigDave muslim people are sharing gifts anytime, because giving a gift to a friend (muslim or non-muslim) for the sake of Allah (God) is a good deed.
and the way of giving gifts in occasions like "Eid al-fitr" or any other islamic occasion, varies from country to another, in middle east they give money to children, you don't know how much these children would be happy to have a big amount of money they never dream to have it.
4. What are the rules of fasting? Can I invite them to a meal, and if I do, are there certain times of day to break the fast?
this is a very good question BigDave, I like it
Fasting the month of Ramadan is a great worship. The following Qudsiyy hadith is sufficient to show the merit of Ramadan:
which means: <<All the deeds of the son of Adam are his except fasting--it is for Me and I reward for it.>> Fasting Ramadan is among the best acts of obedience, among the greatest deeds, and one of the most important matters of Islam.
Allah (God) revealed in the Qur'an a set of rules clear of falsehood for determining the beginning and ending of the month of Ramadan. Moreover, Allah revealed this method and set of rules on the tongue of His Prophet, who did not speak out of his own. Jibril descended to Prophet Muhammad with the Sunnah as well as with the Qur'an. The Muslims took these rules from the Prophet and implemented them from the time of the Prophet until our days.
Every accountable Muslim is obligated to fast the month of Ramadan.
The integrals of fasting are two:
1. Each night to make the intention to fast the following day of Ramadan.
2. To abstain, during the time from the dawn until sunset, from inserting any substance into the head or the body cavity through an open inlet, excluding one's pure, tahir saliva while still inside the mouth, from sexual intercourse, masturbation, inducing vomit, and apostasy.
so my friend BigDave you can invite them to a good and delicious meal at the time of "sunset" it would be great :thumbsup
we will be happy to answer any other questions, and I ask Allah (GOD) to guide you and me to the truth ...
see you later BigDave :wave2
