AFAIK:
The obvious divisor is Buy side, who look to make investments for themselves /on behalf of their clients. Opposed to this is Sell side, who will telephone all sorts of people in an attempt to push a deal through and pick up the comms.
Brokers sort of fill in the gap; Both Buy side traders and Sell side salesman, in the process of completing an order they've been given to complete by some higher being (pbuh), will telephone a variety of people (e.g. MM's, Brokers etc..) to seek liquidity.
Say for example, A fund manager (B) wants to increase his exposure to the oil markets. He will tell his equities trading desk to pick up 400,000 BP shares at VWAP or best. These Buy side traders then call up some Market Makers and Brokers, and say "whats the price for this deal?" The Market makers will look at the position of their firm, and the brokers will consider the positions and sentiment of some of their other clients (for simplicity let's say the MM was at lunch and unavailable. Wholly unrealistic but there you go). Now the broker knows of another Fund (S), that, having been duped into selling 600,000 BP by a very expensive research company, has some liquidity. The Broker then deals with the Buy side trader, immediately telephones the unfortunate seller, and buys out some of their long 600,0000 BP position at a better price than they sold it to Fund (B) + comms.
To surmise:
Traders get told what to buy and sell, by very clever people, and get paid alot for doing it at the best possible price.
Salesman get paid alot, by very clever people, for thinking up lots of new and exciting ways to make their customers buy or sell something at the worst possible price.
Brokers and MM's pick up a little profit, very often, for meeting supply with demand. Overall their exposure is very little.
Now this is grossly simplified; in reality there are Buy side traders, Sales traders, Prop traders, Execution Traders, Brokers, MM's, more sorts than liquorice - and in some cases doing exactly the same thing. Most of the "legacy" names do all of them (hence chinese walls), but some firms do specialise. Apologies for the convoluted response, but I hope it helps clear things up.
In answer to your questions:
How hard is it to get into this field?
Very.
Im not a graduate, are my chances limited because of this?
Yes.
Are there many female workers in the stock market??
There are some, but few in the roles described:
Essex and the City: my life as a ‘posh bird’ broker | The Spectator
(a little out of context in this case, but here it is anyway)
Do all brokers need to pass FSA exams?
Unsure of the regs, but it doesn't matter. You need them.
It's not my intention to discourage you, I'm just speaking plainly. Good Luck.