Again as with the gutter this can be cut easily with a hacksaw and deburred with a half round file.
Cut hole in gutter for downpipe.
In each corner of the outline you made of the sleeve drill one hole.
Start by removing the old downspout.
Use the new 3 x 4 in.
How to cut and install a gutter outlet.
Its easy less than 30 minutes and under 30 00 in parts.
Gutters over flows add downspout to bring water down from roof faster.
1 1 2 x 8s screws should be sufficient to hold the clips and pipe in place securely.
Drop outlet that you buy with your new downspout as a template to trace an outline for the larger hole.
This is the thing that connects the gutter and downspout together so it is important that it is placed correctly and securely.
Depends on where the downpipe fits the gutter mine at home fix into the bottom of the back face of the gutter thus thru the fascia too and into the soffit area out of site until they come down against the brick wall as you said can cut a hole in the bottom of the gutter but the the soffit lining of the eaves wont hide it.
On the bottom of the gutter itself take a pencil or marker and trace the outline of a sleeve.
You can cut out the larger hole with a tin snips or you could use an oscillating multi tool equipped with a metal cutting blade.
Cut the tracing for the connector with a pair of sheet metal cutters.
Clean the area around the hole with a shop rag inside the gutter and ensure that the area is dry.
Starting from the highest point on the downpipe fix the clips to the wall using rawlplugs and screws.