Wow. I applaud you for your bravery.
And I will certainly pray for you and your family, specifically for your Mother’s conversion.
On your question, are you just wondering the difference between the Catholic and Protestant bible? As far as the books contained? If so, that’s a fairly easy one:
Catholics don’t subscribe to the Protestant revisions. Catholics base the Old Testament on the Septuagint. A common misconception by Protestants is that Catholics use a “different” bible. That couldn’t be further from the truth. We use the same bible, but we include the books that Protestants removed during the reformation.
The 7 books removed during the reformation were:
1st and 2nd Maccabees, Baruch, Tobit, Judith, The Wisdom of Solomon and Sirach.
Additions to Esther, and the stories of Susanna and Bel and the Dragon which are included in Daniel may also be different. Orthodox Old Testaments include these plus 1st and 2nd Esdras, Prayer of Manasseh, Psalm 151 and 3rd Maccabees.
As for spreading the gospel and evangelizing, it’s a difficult thing to offer advice on to a 15-year old still living under his parent’s roof. Getting you in hot water with your parents is the last thing I (or likely anybody else) would ever want to do.
Personally, my advice would be to avoid evangelizism as best you can for the time being and focus on your own spiritual growth. Study the Catholic faith. Learn as much as you can about why we do the things we do and believe the things we believe. Investigate the history/catechism of the church, including the various councils. Be certain to know as much as you possibly can before you even think about evangelizing. Then when you are ready to spread the gospel, you will be prepared.
Ultimately though, I don’t know if trying to “hide” this from your Mom is the best way to go. Remember:
“For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it.” Matthew 16:25
If this is truly what you believe, then what a shame it would be to have to lie about it to the people who you love the most. Maybe you can try to discuss these issues with a level head and try to discover sound logic behind why your Mom feels the way she does. Maybe you could even try reading through some apologetics together? Who knows, by the time it’s all said and done, maybe you will make a convert out of her!
I hope I have helped at least a little.
As I said, I will surely pray for you and your family.