Regarding Insecurity...

Depends on if the insecurity is my own or the other person's.

If it is mine, the first thing I do is determine if it is a rational one to have or irrational. If it is irrational, I do whatever I can to overcome it. If I cannot, I am openly honest about it with the other person in the relationship with the tag that, "I know this insecurity is irrational..."

If it is a 'rational' insecurity, I ask myself what options do I have myself to overcome it myself, or should I be trying to overcome it at all? Some insecurities are actually defense mechanisms that are healthy. That help you realize it might be best to redefine the relationship that is causing it.

That said, if the insecurity is the part of the other person. I initially try to be understanding and compassionate, and definitely do not try to patronize them. If theirs is an 'irrational' one, are their changes in my behavior that are worth making (that are easy to make, that doesn't feel like a huge loss by making, and really helps to make the other person feel better) I tend to make it if it is just one thing. If making the change leads to new insecurities, again I tend to start asking if the relationship needs to be redefined.

Now if their insecurities are rational ones, big ticket items that need to be addressed. Are the insecurities regarding parts of me that are not easily changed, ie not necessarily flaws or vices I have but rather natural character traits. In these cases, having honest dialogue that these things are not easily changed. Try to be patient and work through it with them, but know the issue is probably never going to go away by any effort I make.

If it is an insecurity regarding a character flaw or vice, I thank them for the insecurity and use it to help strengthen my resolve to overcome said flaw or vice.

Insecurity on either side of a relationship can fester and poison a relationship, so I've always tried to get in front if them early. Even if it means watching the relationship end because of it.