Always a cause for consternation.
Before I go to your specific questions, you mention children (plural). If your wife meets the requirements for automatically passing USC to the children, the children are also USCs. Did these children have US Social Security numbers during the tax years in question? If so, and if your wife's income was not great, she may qualify as filing "Head of Household". I believe the threshold for HoH is higher than for "Married Separate", and may exceed her income, in which case filing would not have been mandatory.
If the above is not the case:
1. - The Streamlined Procedure is one option for her situation. BUT, please see [*A] below.
Your wife will likely qualify for FEIE (Foreign Earned Income Exclusion), or, as an alternative, she will have paid UK tax and that tax can offset US tax due by use of FTC (Foreign Tax Credits). There should be no need for the questions on union dues or NI contributions (you declare gross income), but let's continue.
2. - UK National Insurance contributions - No.
Union dues - I'll take a stab at this, but warning, I may be wrong. No, unless she were to use "Itemised Deductions" (Schedule A) in which case she may possibly be allowed to use them (and it's here that I'm uncertain. I'm sure others will correct me.) It's unusual for someone in your wife's position to use itemised deductions. Most use the standard deductions instead.
Pension contributions - You'll find different views on this, so I'll leave it to others to comment. The different reasons for either Yes or No (and both may be argued) can be slightly complex.
3. - You may utilise either method, but, assuming you will complete and file the delinquent tax returns soon, doing everything at once works quite efficiently. Subject to [*A].
4. - "In general" (and assuming the transfer of funds [gifts?] do not exceed form 3520 thresholds) the key reporting requirement is for your wife to report the balance, either at 31 Dec. or if higher during the year, for ANY account for which she has signature authority, on an FBAR (if aggregate total is over $10,000) and possibly form 8938.
[*A] If using the Streamlined method, your wife will have to sign a statement claiming the filling ommission was non-wilful. You have a complication in that your wife has, in the past, filled US returns from abroad, and therefore should have known of the requirement to file. This may render the "non-wilful" claim void.
(IMO) Given the situation [*A], it may be best to contact a dual qualified US/UK advisor prior to doing anything at all. They may well suggest others methods of coming back into compliance. Be careful, and make sure the advisor has your best "financial" interests in mind as well as your best "compliance" interests. Hint - a "quiet" filing might be preferable.
Make sure you understand all the options available, and their consequences, before proceeding.