Unless you are using rental income in order to help yourself qualify (like in the situation where you owe a rental property), VA mortgages do not require you have any assets, you could literally be flat broke, not a dollar in your bank accounts, and be fine to get a VA loan.
However having liquid assets will always be helpful, as it is called a "compensating factor" and is one of a variety of ways to make an underwriter feel more comfortable with your loan. For example I had a VA client with a debt to income ratio over 50% and our underwriter required we document compensating factors in order for the loan to get approved - one of the compensating factors was funds in a retirement account.
So to answer your other questions, yes, 60% of the vested amount in retirement accounts can be used as liquid assets when qualifying for a VA loan. You also must be able to access the funds without retiring, etc. (so in a situation where it's a pension that can't be touched until retirement, that can't be used). If it's a regular 401k or IRA those usually have no problem being used.