How the retail forex brokers operate and what they do with the client money?

They hedge themselves on the "real" FX markets - by actually trading the amount of money you dealt with in your trade. As most internet FX trading is all geared, most of the reputable FX dealers are associated or partnered with a back or investment bank that guarantees those "loans" in your leveraged trade.

They keep client money in a trust account, if you are profit and you close out your position, you get paid your profit and your capital returned. If you realise a loss, you pay out the loss out of your capital and more if you aren't protected.

Some brokers trade "naked" but I'd rather stay away from those kinds. That is without hedging their position in the market or by executing the position that their client takes in the market.