Well, your Greyhound experience will most likely be an adventure! I haven't been on one in this country, but my husband and numerous friends have, and there are evidently some interesting characters aboard. I'm sure you'll be fine though, and it is an economical way to travel.
It is always considered thoughtful to bring a "hostess gift" to the person or people where you're staying. Yes, if you are invited to their home in Montana, they most likely intend for you to stay at their home or they should make it clear up front they want you to stay in a hotel. This sounds like you're expected to stay with them. For a hostess gift, you can take just about anything. You can't go wrong or offend anyone with a nice set of kitchen towels or bath soaps or a serving dish or pretty plant -just a little something to say, "Thanks." You can find all sorts of great hostess gift items in the housewares department of TJ Maxx!
Three days should be just right. There's a saying from one of our founders (Benjamin Franklin) here in the U.S. -"Guests and fish stink after 3 days." Unless they've made it clear that they want you there for longer, that's a good time.
As far as questions -I don't think most Americans would be offended with being asked if they were married or how many children they have. I guess it depends on the situation and setting. Questions to stay away from here usually revolve around bluntly asking people what their religion is, what their political persuasion is (are they Republican or Democrat) -or who they voted for, how old they are and anything to do with body image -how much they weigh -that type of thing. It's considered rude to comment on someone's size or any noticeable problem, and in many cultures it's not. You don't want to say, "Wow -you're a big woman!" or "Have you always had hair on your upper lip?" or "We think large moles on the face are a sign of good luck!" -that type of thing. We also don't talk openly (usually) about bathroom things or those parts of the body, although I've noticed much less of a taboo in other cultures regarding things like constipation/diarrhea, bowels in general, gas, hemorrhoids, etc. Unfortunately age is not valued here as much as it is in other areas of the world. You don't want to tell someone you thought they were much older than they are -they won't consider it a compliment.
Paying -always be prepared to pay and offer to pay for yourselves. If you have the money to take them to dinner one night while you're there, it would be a nice gesture, but DO NOT feel like you need to do this -just always offer to pay for your family whenever you do something that costs money.
Keep your bedroom neat and pick up after yourselves and kids -hang towels up in the bathroom, keep clothes picked up off the floor and toys, make up your beds in the morning. Offer to help clean the dishes after a meal or offer to help cook, but don't be offended if the host doesn't let you help.
You can certainly offer to give your hostess a massage. This is really an individual thing as to whether or not she would be comfortable with it. Some would -some wouldn't, but it is a nice offer. For instance -I love massages, but I don't want one from someone I know personally, although many people I know don't mind. My mother-in-law HATES any kind of massage, so you just never know.
You can always start conversations about where they grew up, where they went to college if they did, how did they decide on Bozeman -or have they always lived there, where have they traveled, etc. I'm sure they'll want to hear all about Indonesia as well!
Montana is GORGEOUS and should provide some heat relief for you! Just go and enjoy. You sound like a very thoughtful person, and I'm sure that will come through. They know you're from a different culture as well, so I'm sure they don't expect you to act just like you were born and raised here. Have fun!