A friend of mine is interested in assuming a VA loan. The remaining loan amount is $104k and the SFH was originally purchased at around $125k. my question is, if the mortgage gets put into his name, does he pay the owner the ~$20k for the equity or does the home owner get nothing?

Also, sense he is not the original debater, would he be required to move into the property or could be immediately start renting it out?

You mention the price it was purchased for.  Interesting data, but largely irrelevant.  What price would your friend pay for this property?  That's the key, not the price the seller paid.  

The assumed loan is no different than getting a new loan.  If the sales price is $125K, the buyer would need to bring $125K plus costs minus the current balance of the assumed loan.

Not an expert on VA terms, but I think those do apply to the person assuming the loan.

It depends on what the seller is willing to accept.  Maybe $5k, or maybe $100k.

In a few years when we sell our house I might let the buyer assume my loan. I have an 30 year VA loan at 2.875% which might be a nice selling feature depending on what the average interest rate in 3 years. However the sale price should be ~$100,000 more than my balance so the person might have to get 2 loans and it could actually be more complicated.