When installing a service pack on one instance will this hinder the running of the other instances on a standalone SQL Server? I have a SQL Server 2016 with an instance A and an instance B. Both have SP1 installed, no reporting server.

Can I assume that, when I install SP2 on instance B only, that, while installing, the running of instance A will not be hindered ? (no restarting of the SQL Server service)

Since sqlbrowser is a shared feature, it will also be updated, will this hinder any remote access to instance A (fix port) for the time of the install?
The Service Pack installation process will identify if there are any files in use that will necessitate a restart of the server.

Each instance has it's own independent set of executables, so instance B should not be affected by installation of a new service pack on instance A.

The SQL Server Browser Service will be restarted pretty quickly, however there may be a short period of time where name resolution for named instances may not work as expected.

Best practice for this kind of work on a production server is to schedule it to occur during a period of low or no activity.