My girlfriend’s brother has a problem with me because we have known each other for a long time, and he knows I was in a relationship with a girl for four years. It ended a year ago, after which I began dating his sister, and he doesn’t trust me because he thinks I am the kind of person who will dump his sister at the earliest opportunity. I think he is being unfair because he has no reason to doubt me and cannot use my past to assume I will hurt his sister in any way. I love my girlfriend a lot and she is aware of my previous relationship, so I can’t figure out why her brother needs to have an opinion to begin with. I am worried that this will affect how his sister looks at me, which may eventually harm our bond. How do I fix this?
You can try speaking to him and airing those doubts, for a start. If he is worried about his sister, it isn’t an unnatural thing for a brother to do. If he wants clarity, you can always tell him how you feel about her and why your previous relationship doesn’t define the current one. Ultimately, it is a question of him getting used to the idea and developing a sense of comfort based upon how you treat his sister. If she is happy and convinces him that this is working, he will resolve all the questions he currently 
has on his own.

Is it okay for me to ask my girlfriend out on a holiday if we have only been dating for three months? She may think it’s too soon and I don’t want to put any pressure on her. I think some time off will be good for us, but I am worried about being too hasty.
You won’t know until you have that conversation with her. If she isn’t comfortable, prepare yourself for it, and understand that she may simply need more time, which is okay.