Others pretty much have answered your questions, but here's a recap (I might be wrong but this is what I understood so far):
Stage 1 & 2: These are differentiated based on the invasion of the tumor, that is, how far it has grown into tissue.
Stage 3: If lymph nodes are involved, it's stage 3.
Stage 4: If other organs are involved, it's stage 4 (it doesn't matter if lymph nodes are involved or not).
Cancer cells usually wander around the body and sometimes they form new tumors. Even if liver mets and the tumor in the colon are removed, chemo makes sure to clear those remaining wandering cancerous cells. It also takes care of smaller things that don't show up in CT/PET/MR.
They will likely wait for your mom to recover from surgery before they give her chemo. My mom's liver mets were initially going to be removed during her colon surgery too, but her surgeon discovered new mets during surgery so now she'll start chemo to see how they react. And I would also like to say that your mom is lucky to have her mets and colon tumor removed at the same time! This is a terrible path, but it's a great start!
Caregiver to my super-mom (62), diagnosed Dec 2018
Sigmoid colon, Stage IV
G3, Poorly differentiated adenocarcinoma (5,5 x 4 x 1 cm)
13 positive out of 23 lymph nodes, largest one 1,8 cm
4(?) mets in liver, located at Segment 3 & 7, largest one 2 cm
LVI & PNI present
Clear surgical margins
MSS, KRAS G13D mutant
Laparoscopic anterior resection, Jan 2019
First chemo 11 Feb 2019 (Folfox).