Let me start off by saying you should not be worried about being "frowned upon" for your personal background and beliefs. The Mormon community is filled with people of all backgrounds and opinions. You will be accepted for who you are. 
 
Now, for the specific questions. There is no specific ban on tatoos in the church, especially on those obtained prior to being baptized. There is no requirement that a person have them removed upon joining the church either. The church's viewpoint regarding tattoos is that the body is sacred, a temple where the Spirit of God may dwell, and as such we should respect and care for it and not deface it. Therefore the church highly recommends that we no get tattoos or multiple body piercings simply out of respect for God's handiwork. Many members choose to have old tattoos removed out of this respect for their body as well as out of self-consciousness and a desire to blend in, being in an environment where tattoos are not common and may stick out. 
 
Regarding coffee, when a person is baptized, they make a covenant to obey the commandments, one of which is the Word of Wisdom which counsels against coffee, tea, alcohol, tobacco and other such harmful or addictive substances. That said, there are many members which do partake of some of these substances. While taking these substances may not keep you from being a Mormon, they may hold you back from some of the blessings and opportunies available to those who do adhere to these commandments. In particular, to be able to participate in the Temple ordinances and gain the blessings there, one must be obey the Word of Wisdom. I once heard of the story of a person who asked the bishop, "Are you really going to keep me out of the temple because of a cup of coffee?". The bishop responded, "Are you really going to keep yourself out of the temple because of a cup of coffee?" You really need to decide, what is more important? 
 
Lastly regarding tithing. I certainly understand the sentiment of "I worked hard for this money, now you want me to give it to these guys?" I think that it really helps when we stop and think about where all of it comes from in the first place. Everything we have in this life, our bodies, our families, our livelyhood, everything in this world was created and given to us by God. The idea that we "earned" it is a falacy. No matter how much good we do in this life, we will always be indebted to God. Tithing is a principle of sacrifice that helps us let go of our attachments to earthly things so that we can lay hold of heavenly things. Tithing does not go to pad the wallets of church leaders, rather it goes to provide us with meetinghouses and temples and activities. It all goes to the benefit of the saints as a whole. It really is the least we can do for all that the church and that God for that matter does for us. 
 
It really does all come down to the principle of sacrifice. The giving up of something we like for something so much more important to us. Joseph Smith once put it this way: 
 
Let us here observe, that a religion that does not require the sacrifice of all things never has power sufficient to produce the faith necessary unto life and salvation

Member of the LDS Church are here to help each other grow in faith in Christ. Not to criticize each other. While tattoos are not officially prohibited it is very frowned upon for a active member to get new tattoos. Past tattoos are not expected to be removed but getting new tattoos is considered in many if not most circles to be a serious transgression.  
 
If you wish to be a active member of the Church you must refrain from all and any form of Coffee and Tea (with the exception of Herbal Teas) there is no negotiation on this, Tobacco, Alcohol, and Coffee/Tea use is a sure way to lose a Temple Recommend and not be a member in good standing.  
 
Tithing is also required to be a member in good standing, yes to many giving 10% back to Heavenly Father might seem like a lot. But remember that everything here is made by HIS hands not ours. We really own him 100% of our wages and efforts. He lovingly though only asks for 10% to teach us to be generous and to she our obedience to him and his Commandments.

I'm considering converting to LDS, but I do have two questions to ask because it is very important to me before I make a decision. 
First of all, I lost a baby a couple of years ago... What will happen to my baby in the Hereafter? 
 
Secondly, as a child I suffered grieviously at the hands of my parents. I was raped by an uncle, and molested by my own father, and my mother accused me of it being my fault even though I was only a child and tried to stop it from happening. I was also beaten frequently and had a few bones broken in the process. As a young adult I made a few bad decisions because of my limited understanding of the world, but have now come out the other side and am trying to make the best possible life for my children and myself.  
I guess what I want to ask is why do these things happen? Why does God allow these things to happen? I felt for a long time that God must hate me, or abandoned me even though I prayed and prayed to Him to rescue me and to heal the painful wounds that are still left from those experiences. Does He really love all of us? If He does, then why does He allow children to go through such horrible experiences?  
Will He heal my wounds and take away the pain of remembering those experiences? 
Thank you for your time and your patience,  
FarFarAway