Single service account running all SQL Servers
Is there any negative performance impact for using the same service account and agent account to run SQL Server and SQL Agent respectively for all SQL server instances running at a small company of say 35 servers? 


No. Service accounts do not affect performance in any way. Its all about security !

From the SQL Server 2012 security best practice whitepaper (warning: word doc) :


  When choosing service accounts, consider the principle of least privilege. The service account should have exactly the privileges that it needs to do its job and no more privileges. 
  
  You also need to consider account isolation; the service accounts should not only be different from one another, they should not be used by any other service on the same server. 


If you are running Windows Server 2008 R2 &amp; SQL Server 2012 and up, then best is to use 


Virtual accounts or


  Virtual accounts are managed local accounts that is automatically provisioned and managed. In SQL Server 2012, they are the default service account specified during setup. It can access the network. A virtual service account has a well-known name in the form of NT SERVICE\ and can access the network using the credentials \$. 

managed service accounts


  A managed service account is a special type of domain account that can be assigned to a single computer and used to manage a service. It must be provisioned by the domain administrator prior to being used. This type of account cannot be used to log in to a computer and provides automatic SPN and password management, once provisioned.