No, you do not need to install anything or have your computer running for trading to work. The trading system ("Eden") itself runs on a system of advanced central server computers and nothing is done locally on your own computer. However, you may want to connect your own trading account to your computer and/or mobile phone to be able to quickly check your current account balance etc. This is done by installing the user client/app for the Metatrader 4 (MT4) trading platform and from there log in to your trading account with the broker. 

If you want to see the status of your crypto account with Liquidity One, you can do so by logging in to their website from any browser.

Corresponding information on the status of your trading accounts is also available via the Mobile Wealth customer portal.