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She should file tax returns for any years in which she had income above the tax filing threshold for her family size. She can check with a tax professional to determine whether she was required to file. Income level determines the requirement to file. Not everybody is required to file a tax return.
Probably not applicable in this case but the source of income also has a bearing on the tax filing requirment. For example, Military disability recipients don't ned to file tax returns if that's their only source of income, regardless of how much it is. Be careful about blanket statements.

As she has a co-sponsor, it is not that important that she show current and on-going income. However, unless she made no money, she must file tax returns.

You can start by gathering applicant documents since these take time to put together. You should get the email some time next week since this week is short due to July 4 Holiday. There numerous links on here for the i230 check list so you should check them out and strt getting the docs together.

130 petitions out of local offices have irregular forwarding to nvc.. it can take from a week to three months until it gets there without any outside help
nvc will request that you scan and email your noa2 to research.. they will come back in three weeks and say they don't have it. that means your petition is stuck somewhere between your local office, nrc and nvc
you will only know you petition is at nvc by calling or waiting for their letter to come
once you have your case you give them your email and the beneficiary's email and all future correspondence is by email
all mail will be sent to the address you originally gave them
there is no ep for india that I see on the nvc site
go to the nvc threads for all you step by steps
your situation is common and you can read about other's experiences there

1) NVC would contact you by mail if they do not have your email addresses
2) They would mail her to her home residence that was stated on the I-130 petition
3) Electronic processing is NOT available for India.
4) Keep calling the NVC until your case arrives there. If it hasn't arrived there in another week I suggest the USC call the USCIS and speak to a tier 2, ISO. That person can find out if the case has left the USCIS yet and where it's supposed to be headed. Because your USC wife is not in the US, making an infopass is not an option for you so calling is the best thing for you to do. Keep in mind it can take up to 90 days to make it from the USCIS to the NVC even with help but it's best to be on top of this process if it takes a month or more to get moving.

She would have to move to a state that allows first cousin marriage before she starts filling for your I-130

You will have to reside in a state that allows first cousin marriage.

It will be a positive thing as long as you have a co-sponsor, because time spent together looks good on your application and shows you are serious about the marriage.