Spreading payments is good for reducing risk. Have a look at Legal and General products to start off with, they're fees are low especially for trackers.
The shares are issued by the company itself like a form of currency if you like, this is called an IPO. Initial purchase offer, they have no guaranteed value exactly since obviously the company can go broke. You may get a yearly cut of the profits but theres no guarantee of that even if they do well, its their choice.
The price is decided by the market mainly (how well is the company doing), theres always a customer for the right price thats where your broker comes in since you are just a little fish.
The company uses the shares to fund itself partly, it may buy shares back and it may issue/sell more to raise capital.
If you are new to the game you should invest generally via a company managed fund or unit trust, they will charge a % fee yearly, initally and even to withdraw but its worth it if you are not sure. Trackers are the cheapest, they are like bots just following the market blindly, up and down. People often fail to outperform them