Checking on Friends, Onward to Sector 7, Crawling to the Surface, and Home Is Where the Heart Is are quests in Chapter 13, "A Broken World", in Final Fantasy VII Remake. Cloud Strife, Tifa Lockhart, and Barret Wallace travel to Sector 7 to investigate the damages.
Walkthrough[]
There is a mythical amulet in the upstairs of Aerith Gainsborough's house that can be picked up.
Travel through Sector 6 and head to the southeast exit. At the fork in the road, head west through a tunnel. The route here through the Collapsed Expressway is similar to that in "The Town That Never Sleeps"; head forward (southeast on the map) through the same path, and though gorgers are fought, they represent little threat. Eventually, the original route is blocked; head left instead to the Old Bypass of the Collapsed Expressway.
Down this path, ringmaws are fought; these are fairly durable enemies that can stun a character, but can be defeated with simple abilities. At a fork in the road, with one path leading down a tunnel and another through open ground, both paths lead the same place and neither have anything unique. After this, varghidpolis and terpsicolt enemies are also fought; these are fairly durable enemies but can nonetheless be defeated with normal abilities. Terpiscolts can spin while flying quickly, meaning Tifa and Cloud cannot attack them, though Barret can use his attacks to pressure them.
Further down the path, a Sweeper Prototype and a Smogger are fought. 
Lightning Materia should be equipped before fighting them, along with Cleansing Materia and Revival Materia. The Smogger can be defeated fairly quickly with melee abilities from Cloud and Tifa. The Sweeper Prototype's speeding attacks must be avoided, or absorbed by Barret's Lifesaver, and lightning spells can be cast against it to pressure it and then destroy it with abilities.
Heavy-duty bracer.
Once both are destroyed, proceed forward down a ladder to a bandit hideout. Down a hallway on the left, a heavy-duty bracer can be found , providing great defensive stats and three materia slots, making it ideal for Barret. To progress, take the path right down a narrow path to where bandits are fought. These can be dispatched with normal abilities, though the 
Fire Materia is useful against them. Proceeding further down the path, defeat two more bandits, then head right and at the back is a chest with an ether. Proceed south, and Beck, Burke, Butch, and the Grungy Bandit are fought again. Beck, Burke, and Butch can be defeated quickly with abilities from Cloud and Tifa, allowing the party to focus the Grungy Bandit; overwhelm it with damage and spells to defeat it. Head further in and obtain the orb of gravity from the chest and use the ladder to climb out.
NPCs at the Sector 6 park.
After climbing the ladder, more ringmaws are fought, and after this, the follow a linear path to leave the expressway, leading to Sector 6. A cutscene commences, after a few non-player characters can be talked to. The item store owner sells the 
On Our Way disc, and a bench fully heals. The weapons vendor sells 
Big Bertha for Barret, as well as several new pieces of armor: the Gothic Bangle, Magician's Bracelet, the Heavy-Duty Bracer, and the Sorcerer's Armlet. Magician's Bracelet and Sorcerer's Armlet can be ideal for Cloud or Aerith for magic, where the former is better for equipping spells while the latter is better for defense. Heavy-Duty Bracer is ideal for Barret or Tifa, and can also be useful on Cloud if he is used more for damage. To proceed with the quest, interact with the slide and select "Yes" when asked to head underground, commencing a cutscene, after which the party goes to the S7-6 Service Tunnel.
In the service tunnel, head down the linear path, following Barret. When Barret uses a ladder, follow him up and head out the tunnel, leading to a cutscene. After this, follow Barret through the rubble, leading to another cutscene. Push down the wall with Barret's help and follow the cat down to a ditch in the ground, commencing "In Solitude".
Hard mode tips[]
It is only necessary to save MP on Barret, and Cloud and Tifa can cast as many spells as they wish. Lightning materia is ideal against the Sweeper Prototype and smogger and against Beck's Badasses, though these fights are not considerably harder than before. Barret's Lifesaver can be used if the fights present difficulty.