Yes. As far as i have understood uniswapn is an automated market making service so pooled liquidity is there for most tokens that you can trade. Without liquidity pool there is no way to buy or sell on uniswap. Due to returns most tokens are available in the pool as hodlers park there to get returns for hodling.
Almost right. Liquidity pools are provided for the community by the community members and they're granted with liquidity provider fees for that.
It is true for most of tokens that are listed on uniswap, thus service is indeed decentralized and somewhat secured