The bottom inner adhesive layer reaches higher than what you see in the diagram above, so you will have to insert the pick deeper at the bottom and the sides along the bottom to separate the inner adhesive area. Just don't force the corners of the covers upward too much to keep from cracking the glass.

Aside from the left edge where the fingerprint sensor cable is, you may have to insert the pick up to 2cm on the sides and top, and a little further along the bottom, and swipe sideways to separate the inner adhesive areas. If one side doesn't separate fully, just apply heat, insert the pick deeper into the phone, and swipe sideways until the back cover detaches. There isn't a need to apply much vertical force, especially on the corners, since the cover will just pop up once all the adhesive has been sliced by the pick.

While testing the phone after battery replacement, but before reattaching the back cover, if a thermal warning (triangular thermometer icon) appears during charging that prevents charging over 50%, remove the charging cable and use a lightly warmed iOpener or heat gun on the battery to warm it slightly. Once the battery is warmed up a little, reattach the charging cable, and the error should go away. Battery charging can be resumed. This assumes no hardware was damaged during battery replacement.

Use tweezers remove any inner adhesive strips that may have started peeling off when the back cover is removed, or adhesive clumps. If an adhesive starts to peel off, use tweezers to pull the strip off completely, and then replace only that removed adhesive strip. Actually, the iFixIt inner adhesive strips don't seem to have the white non-stick areas that are on the original adhesive strips. Thus, it seems ok to keep the original inner adhesive strips if still attached to the phone.

The outer adhesive border is like a good, not a strip, and should be replaced. Using isopropyl alcohol to rub off only the edge adhesive on the phone and back cover works well.

After adding a new outer adhesive and reattaching the back cover, you have one try to align and replace the cover. The cover might not attach flush onto the phone with no side gaps, due to the outer adhesive strip placement. It is probably sufficient if the outer adhesive seals all the way around the back cover border.

If you plan to replace the battery adhesive, the adhesive doesn't seem to stick to the battery directly, so I instead stuck it into the battery compartment over the existing adhesive, and then placed the battery on top.

When reinserting the new battery, you may want to push the the battery higher up in the compartment, so that the battery cable more easily aligns with the connector on the phone. It may take a few tries to align the battery perfectly. Even with the new adhesive, the battery doesn't stick much, which is fine, so that it can come out more easily next time. It's enough to maintain friction to not move around I think.

If this is your first battery swap for the phone, consider peeling off the Note product sticker from the old battery and reattaching it to the new battery if you want to keep it.

The iFixIt suction cup doesn't work, as stated in the other comment. After injecting the alcohol, you can insert a spudger into the hold at the top-left corner of the battery. It seems like this hole was made for the purpose of popping out the battery. You could probably also use a pick on the bottom center of the battery to pop it out. Just pull it out slowly.

The tool list includes a disposable adhesive remover in a dropper bottle, but you might want to find a reusable syringe-like dispenser bottle separately, as shown in the photo to better inject alcohol into the gap.

You can actually leave the right side of the coil attached to the phone so that it is easier to align and reattach afterward.