Is there any publicly available dataset that provides internationally-comparative economic variables, including government expenditure, population, territorial size, per capita GDP, trade, infrastructure, conflict events, etc from 2000 onwards ?
You will get data for almost all the mentioned variables on World Development Indicators, Word Bank database. https://databank.worldbank.org/source/world-development-indicators
For trade volume related data- Several database are available such as UN-Comtrade, ITC Trade Map, WTO Database.