Once you're fat adapted, you can try carb cycling for the long term, it helps you avoid any of the negative effects of constant ketosis, and in fact more accurately reflects the way pre-agricultural people ate.
As for the GI stuff, if you are not used to eating high fat, you will not produce enough bile acids to properly emulsify it and digest it, so some of the undigested fat will get into your gut and the microbes there will have a field day with it...once you ramp up, it usually goes away, as you've seen. It wouldn't hurt to take a quality probiotic though, or have probiotic foods like homemade sauerkraut, kim chi, kefir or kombucha.
If your family is really concerned about cholesterol, I would recommend the following book; it's very normie friendly. My local library has it, see if yours does. it does a great job debunking the saturated fat - cholesterol issue.
As for the raw eggs, they are actually very good for you; you just have to get high quality organic eggs from chickens that have been reasonably treated - i.e not confined to a small cage for their entire lives.
