Can you have a Roth at different places; for example, one Roth IRA account at Fidelity and one at Vanguard? 

Absolutely.  Assuming he intends to contribute the max of $5000 annually, he could do $2500 at each brokerage, or $1000 and $4000, or $2000 and $3000...

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Edited to add: 

One thing to keep in mind, the minimum purchase for the no-load funds that he's interested in.  Most mutual funds have a minimum initial investment of $1000 for IRA accounts.  So if he starts the new account with only $500, he may not be able to do much with it.  That's especially relevant if considering Vanguard funds - many of their funds have a ridiculous minimum investment of $3000!