The issue would be the arrest. The use of fraudulent documents to obtain an immigration benefit would be a problem if it were to obtain a U.S. immigration benefit, which it wasn't, and the UK subsequently granted her citizenship, so that one shouldn't be a problem. However, the arrest needs to be evaluated. Obtain all the documentation regarding that case including the exact charge and citation to the section of law (so that an attorney can research it), as well as the sentence, and...
Seattle is very good on these issues, and really tries to be accommodating, but it does depend on their workload. As long as you have an appointment notice (even if for a different day), you can attempt to do it as a walk-in, but you should arrive extremely early, and be prepared to wait. If they can get you in, they will. An option is to reschedule the appointment.
When you receive the receipt notice, the top section will have a receipt number. The receipt number is the case number. If the person you are petitioning for will need to consular process abroad, when the petition is approved and transferred to the National Visa Center, it will be assigned another case number. That one will be on correspondence from the NVC. It would help to have an immigration attorney take you through the process
If the government is not opposed, the judge is very likely to grant it. I would continue to prepare, anyway. You want to submit all evidence and make a complete record for the future just in case. The judge can still deny it, but it would be extremely rare
Oh, my gosh, be careful. If the offense could have been punishable by 365 days in jail, if she could/could have received 365 days in jail (even if she didn't), not only could she be denied citizenship, but she could lose her permanent residency.
You may very well qualify for deferred action, you also may qualify to apply for permanent residence. It is important that you meet with an experienced immigration attorney to discuss the benefits and risks of each option.
Yes. The waiver is part of the overall visa process. It is filed after the I-130 is approved, the file is then transferred to the NVC, you pay the visa fee to the NVC, then you notify NVC you are doing the provisional waiver, then you file the waiver. NVC will hold the visa process while you apply for the waiver. It is a bit complicated. You might benefit from the assistance of an attorney.
There are a couple things here for you to know. When the form asks about children, you are required to list all children regardless of whether they intend to immigrate at that time. Failing to do so can cause problems later on. If you are filing an immigrant visa for this person as your spouse, you need to file separate petition for your step child. Note: however you end up doing it, you will need to show your partner has legal custody of the child and/or is legally allowed to take the kid out...
It is unlikely he would be able to adjust status unless in the meantime Congress passes immigration reform that would give him some alternative. Barring that, he would need to consular process, and may need a waiver of the unlawful presence bar. The waiver is based on hardship to a US citizen or permanent resident parent or spouse. If your brother doesn't have a US citizen or permanent resident parent or spouse at that time, he wouldn't qualify for the waiver.
What type of school are you going to? I haven't heard of schools doing background checks on students before. I agree they are likely to check the fingerprints, so if you were never fingerprinted for immigration and you have no arrest, nothing should show up. I would wonder the purpose of the background check, since I believe it is an unusual request by a school of a student (not an employee). Undocumented persons are allowed to attend grade school and in WA under certain circumstances can...