My tourist visa ran out two months ago, but I am afraid of persecution in my home country and wish to apply for asylum. I have a free lawyer who is helping me prepare the Form I-589 and all the documents showing how dangerous it would be for me to return to my country, but it seems to be taking a long time. She says she is still collecting documents and preparing my written statement. What if I get arrested by Immigration before she turns the application form in?
It's good that you are paying close attention to your case, but don't panic quite yet. If you get arrested by U.S. Immigration and Customs Enforcement (ICE), you will still have the right to a hearing before a judge in Immigration Court. There (assuming your lawyer doesn't wait until a full year has passed since your permitted stay expired), you'll be able to present your full request for asylum.
In fact, many people who apply for asylum and are not approved by the USCIS officer who first hears the case must go to Immigration Court after that to have the case heard again. (Of course, you don't want to do anything risky that brings you to the attention of the immigration authorities, like hanging around a USCIS office or getting arrested by the police.)
What if your case goes to the Immigration Court, but is denied? You would then have the right to appeal and to stay in the United States during that appeal. (You might not have the right to work during that time, unless USCIS is at fault for delays in your case--which is quite possible in 2018, when immigration courts were extremely backlogged.)
It sounds like you are also worried about whether your attorney is doing a good job. A good attorney will take the time to talk to you in depth about the reason you fear returning to your country, and will gather documents such as newspaper articles, reports by human rights organizations, and affidavits by experts in order to back up your story about what happened to you. Hopefully your attorney is doing just that. She is probably also extremely busy.
Again, however, you do need to keep an eye on the one-year deadline on applying for asylum after your entry to the United States. Talk to your lawyer to make sure she is keeping track of this.
If you have seen other signs that your lawyer is not giving your case the attention it deserves, or if a month or more passes without any apparent progress, you might want to ask around (with nonprofit organizations or lawyers who are representing friends of yours) to find out whether your lawyer is highly regarded. If she's not, look for a new lawyer. You can find an immigration attorney by searching Nolo's Lawyer Directory, where you can view in-depth attorney profiles of attorneys in your local area.