No, the demos are always free. Who'd ever pay money for a demo? People use demos to see if the full game is worth buying.
You can download demos
The games that you purchase do not cost anything extra to download them and the demos are free to download. PlayStation Plus customers also have some free games for as long as you are a member of PlayStation Plus
First you need the system updated to be able to go to the Playstation Store and you need to have an account. Demos you do not have to pay for so it is not necessary to have money in your wallet. Of course you needed an internet connection and then at the Playstation store just pick a PSP game demo and you will be able to download it. Myself I use the PS3 because I can store it in the PS3 harddrive.
If you have a playstation network card, you can download anything from the playstation store, as long as you don't exceed the money limit on the card.
the playstation 3 has the playstation network you can buy games off the playstation store as well as the latest movies, in SD, HD you will need a credit card or a ps3 game card with money on it and bump in the code for some full games, others are free as well as many demos and game updates.
From your Playstation Network connection on a PS3 you only need money in your Playstation Wallet from a credit card matching your account or a Playstation Network Card to make a purchase and download it into your PS3 harddrive
... Are you new to games? For PS3 you go to playstation network and download it with money.
Go to a retail store and purchase a Playstation Network Card
No PS3 does not have Live they have the free Playstation Network and for the cost of Live you can purchase Playstation Plus that provides members with free games and reduced download prices. You do not need to join Playstation Plus to play on the internet or use any of the Playstation Network features
First you must have a Playstation Network account and internet connection on your PS3 so you can download items. You can buy items that are free and sold for $0.00 or if you have money in your Playstation Wallet you can purchase items. Money can be put into the wallet with a credit card matching account information or through Playstation Network cards
Playstation Network Cards are not free and do not use virtual money but actual money
Most of the features of PSN are free to use. Online gaming, downloading demos, and PlayStation Home are all at no extra cost to you. There is a paid subscription to PSN called PlayStation Plus, and buying games and add-ons online cost money.