I don't know why people are being difficult, just answer his question....
1 - There are examples of coworkers in a relationship on the same team not having any issue. Two adults can do whatever they want and are a lot of people are mature enough not to have it impact their work. However, may want to consider the power dynamics of their roles. Two physicians on an equal level being in a relationship is different than an authority figure in a relationship with a subordinate. Latter would make me more suspicious but that's not to say it couldn't work either. As for speaking out, if you see red flags, obviously you should speak out or take the time to better understand the situation, but if there doesn't appear something wrong, you don't need to stick your nose in the relationship of two consenting adults.
2 - By nature doctors are compassionate and well-meaning people that want the best for their patients so it's not hard to see why some would want to go beyond their job description and give their patients their personal information. However you also want to maintain good work-life balance, an overworked doctor is not able to provide the best care so while your intentions are good, you may in fact be making things worse by overstretching yourself. Every person decides whats important to them, some people are okay with working more at the expense of family and leisure time whereas other will prioritize their careers and work. Giving your personal information is an individual decision but it's not a part of the job description so you shouldn't judge someone who chooses not to do so.
3 - I don't think its illegal. Gifts can look bad as whenever someone gives something, they tend to expect something in return or it can appear that they are buying influence. Potential for patient mistrust of physicians so if you do have a conflict of interest for example, a drug you are prescribing for your patients, you should at least be upfront about it as they are more likely to appreciate your honesty versus finding out about it. Your first priority is to your patients, not the pharma company. Gifts aren't necessarily bad though as they can play an important role in continuing education for physicians. For eg, there may be a really good drug out there that many physicians would not know if it was not for the pharma company reaching out to them. It also depends on the value of the gifts eg. a $50 meal vs a gifting someone an expensive watch is obviously different. So I wouldn't say its illegal or even unethical unless the aim of the gift is to buy influence.