is the forex price different at different brokers locations?
Yes - slightly. (Shouldn't be "hugely", at least in theory.)
But be aware that when you "trade" against a counterparty "broker", it isn't really a broker in the sense the word's normally used. No currencies really change hands when you "trade" with them: all you're doing is betting with them about the price movements. And be aware that they hold your funds and have their own pricing for their own "products", and they make up all the rules and decide how to interpret them, too.
Unless you have enough funds to trade with a genuine, direct-access brokerage in the interbank market (they execute trades on your behalf in exchange for a commission, and they have no incentive for you to lose, because they're not directly financially involved, themselves, in the
outcomes of your trades).
That said, there are "dreadful" and "not-so-dreadful" spot forex counterparty "brokers" available.
Where, how and by whom they're regulated is very important.
For example if you're in the UK and use an FCA-regulated brokerage, at least the chances of outright fraud and losing your whole account that way are very limited, and you have a government-backed protection guarantee if they disappear with your money.
But in general, you're right to be concerned, and to be very careful.
Always check their
regulatory record as well - not just "by whom they're regulated". There are some
very big, very well-known "brokerages" who have been fined multiple millions by multiple different regulators on multiple occasions in multiple countries, for as many years back as you look, and show no signs at all of changing their behavior.