You need do nothing with regard to her ex-boyfriend and your sister. First, with regard to the home, since she transferred title to you prior to her death, the house belongs to you and you need do nothing further. Second, with regard to the will, you need to file the will with the probate court to have the will validated as your mom's last will and testament and to be officially appointed the executor of the estate. To evidence this, the court will issue you letters testamentary to use in your authority as executor. I know that this seems like a huge hassle when you're the sole beneficiary, but this is for the protection of all involved parties. In order for other parties to be assured that the will is valid and your appointment is valid, those parties need verification from the probate court that this was indeed the valid last will and testament of yourmom and that you are indeed the authorized personal representative as evidenced by letters testamentary issued by the court. Otherwise, these third parties can't be sure that someone else is not going to later claim to have the valid will of your parents and to be the representative. These rules are also in place for your own protection to prevent someone else claiming estate assets.
If the ex-boyfriend or sister want to contest the will, the burden is on them to do so; you have no duty to do anything otherwise. They would have the burden of proving a lack of requisite mental capacity, fraud, coercion, duress, mistake and/or undue influence. It's a high burden that must be met to overturn the will.
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