I want to start by saying how I appreciate your help to others as seen through your web site. My question is: I recently got saved and have been in secular relationships before. There is this lady in our fellowship group whom I am deeply in love with and would wish to start a Christian relationship with her, but I am afraid she might view my reactions as too fast when I approach her. What advice can you give me? Do I inform her? What are the expectations from a Christian relationship?
Your question is a bit difficult to answer because people in general play games with words like "relationship." I've seen it use from a decision to date to having sex. Broad words are often used because people don't want to admit that they are sinning.
The best advise I can give is one found in Song of Solomon 2:7, "I charge you, O daughters of Jerusalem, by the gazelles or by the does of the field, do not stir up nor awaken love until it pleases." There is no need to rush. You can take the time to let a relationship develop. People fall into trouble when they try to make things happen faster. In their rush they do things they should not do at that time.
I assume you've gotten to know this woman and are good friends with her. So ask her out for meals, ask her to join you in doing things, basically find reasons to be able to spend more time with her to get to know her better. When you get to the point that you are certain that she is the kind of lady you want at your side for the rest of your life, then tell her so and ask if she would consent to marry you. Even then, spend some time (I usually recommend a year), of being engaged to make all the preparations for setting up a household together. This would be the time to work out all the problems that are bound to come up, and if they can't be worked out, then don't get married.
Paul told Timothy, to treat "younger women as sisters, with absolute purity" (I Timothy 5:2). Sex and the things related to it are for after marriage, not before. Don't be stirring up passions until the night of your wedding. Treat the woman you love with respect. Be the guardian of her honor, and not her downfall.