I believe I'm on the "old rules," as I applied for my visa before July 2012.
Yes, as long as you applied before July 9th 2012 and your visa is valid for 27 months (not 33 months), you will be under the old rules.
- How much of a problem is it that I cannot get in to take the test until about 3 weeks before my visa expires?
Shouldn't be an issue at all, as long as you pass it and can get the application mailed in/attend an in-person appointment before your visa expires.
If you fail it, you have to wait 7 days before you can take it again.
- Will I be in trouble/illegal/unable to work during the time that my application is being processed if my visa expires in the meantime?
No, your current visa status is extended while your visa is processing, so you can continue to work. Currently, it's taking 4-5 months for ILR postal applications to be processed.
- How complicated and time consuming is the application process?
Not very complicated - in fact, it's much easier than your spousal visa. There's no official income or accommodation requirement.
You just fill out the application, gather the documents (all listed on the application form) and mail it in.
- Is there anything else I should be/ can be doing in the meantime, or must I wait until I take the test?
You will need to gather your documents.
You need to provide 6 official letters in both you and your spouse's names, addressed to you both at the same address, covering the entire 2 years of the visa.
Basically, you need one document in each name for each 4-month period of the last 2 years - either 6 jointly addressed, 12 separately addressed, or a combination of both. They must be from at least 3 different sources and the list of acceptable documents is on the application form (i.e. tenancy agreements, bank statements, utility bills, letters from HMRC/DVLA/NHS etc.).
See here for the application form (with all the documents required listed on it):
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/314891/SET_M__06-14.pdf
