Dyna

That picture you posted shows the first stage of the application, I-130. So after that gets approved, nothing will happen, it only means your sister is officially waiting for her visa slot to open (7-8 years) and then when it's her turn, she will be able to file I-485.
So basically, it will take 7-8 years. 
When your mother becomes a citizen, your sister will automatically get put into "citizen's unmarried sons and daughters" category and it'd speed up the process by a tiny little bit. (maybe 5-6 months faster)
If your sister really wants to come here, go ahead and start the process, it's a long wait and no one really knows if it's certain, but why not? But remember, your sister must remain unmarried during this whole process. 

I think you've mistaken. Your sister is an adult (over 21 years old) so she'd have to wait even longer. So far they're processing Permanent Residents' petitions for adult children for cases submitted around JAN 15, 2011. Which means it'll take around 7-8 years for your sister. 
During the process time, you sister needs to remain unmarried. 

The affidavit of support won't be needed for many years so your mother may have a job by then. 
 
The key point to this type of visa has already been mentioned: your sister must remain unmarried for the entire process. 
 
I also wouldn't be surprised if this category is removed in the near future. 

For you to petition as a sibling would be a wait of 13+ years. 
 
The I-130 at USCIS is just stage one. After it is approved you then have to wait many years for a visa number to become available as there are only a limited number made available each year. 

So like another JFH already answered, that's just stage one of the application.
Here you can find Visa Bulletin.
https://travel.state.gov/content/travel/en/legal/visa-law0/visa-bulletin/2018/visa-bulletin-for-january-2018.html
For a citizen's sibling, they're at 2004 cases now, which means 13-14 years. 
For LPR's adult children, it's 7-8 years.
Btw, both of these categories, like mentioned before, could possibly be cut in the future.

The I-130 is only the first part. That establishes a legal relationship between the petitioner and beneficiary so they can apply for an immigrant visa. The I-130 may only takes a couple years, but the approved petition will just sit there after approval until an immigrant visa number becomes available. That's because the number of immigrant visas available in that category is limited each year.
 
The visa bulletin determines when an immigrant visa is actually available. https://travel.state.gov/content/travel/en/legal/visa-law0/visa-bulletin.html
An unmarried adult child of an LPR is F2B.
An unmarried adult child of a USC is F1.
A married adult child of a USC is F3.
A sibling of a USC is F4.
NOTE: There is no category for an adult child of a married LPR. Marrying while the petitioner is an LPR will void the current petition (even if she is no longer married in the future).

no, it's always going forward, with new ones, they won't canceled the petitions in course
 
but as said, their are 2 bulletins, the first one is the service center where the first form of many, the i130 is processed, as you stated, it can take many years for the first form to be approved
 
then the approved form is sent to the National Visa Center or NVC where it will sit in a pile awaiting priority date for many years, until there is a visa available for your sister
the process currently is around 7 years altogether
 
now, unless the cosponsor lives in the same house and is a direct family member, the other person will file another i864 as your mom's joint sponsor if her income is non existent or not enough.
 
the i864A is for a family member, such a spouse, child or parent, living in the same house to combine income
 
for the i864, the joint sponsor can be any US Citizen or legal resident that has enough income
 
 

It’s debatable
in the past it seems when things have changed they have always grandfathered in everyone waiting, but at least one of the proposals that has been put forward has been to only process those cases with a year or less to wait till a visa number is available and scrap the rest (at the time the new law takes effect). Difficult to say what’s going to happen when lawmakers themselves don’t know.