If anyone inherited say 25,000 should you devide it into 2 different banks?

No reason to use 2 banks unless you want to. Now ... over $250,000 - YES, because FDIC only insures up to $250,000.

it wouldn't be necessary as the FCIC or NCUA insurance is 250,000$

The interest may or may not be the same RATE. Banks have different rates. However, if you receive an inheritance of that size, you will first pay inheritance taxes, so it won't end up being the full $25K anyway. And you might get a real interest bump up if you put all of it into an IRA, or a Certificate of Deposit, or in one institution. Shop around for the best advantage at several banks. 

If you deposit $10K or more into any financial institution, it triggers notice to the IRS in the form of a Currency Transaction Report. The bank is mandated to send that info to the IRS. No report is sent if the amount deposited is under $10K. So if you decide to spread it around, you should keep your deposits under $10K in each institution. 

The interest can vary but the main reason is that you if one of your bank accounts get hacked, they will only get what's in that account.  I would put it in 3 accounts....10K in two banks and 5K in the last one.

No advantage to deposit to two separate banks. In fact you may get a better interest rate on the amount by depositing it in a single account. Some online banks pay higher interest that the brick and mortar ones.

I would deposit into a bank account for a short period of time and to ensure it is easy to move to a high interest source...25k can earn much more elsewhere than low interest bank accounts

Banks set their own interest rates, so the interest between whatever two banks you might choose may not be the same.  Unless it's just something that helps you keep your personal finances organized, there's really no advantage to splitting your money like this.  

No reason to split it up.

No, that's just a slight complication but unnecessary and without any significant benefits. You would also want to put it someplace where it earns more because bank interest is currently extremely low. At least a money market account.

The interest may or may not be the same.

Different banks offer different interest rates and different types of accounts.

A simple savings or checking account will have a different interest rate than a CD - certificate of deposit.

You need to decide if you're going to just let the money sit and accumulate interest or if you'll need access to it.

Many options - best to talk to a banker who can guide you.