Is the Czech Republic a Schengen State?

Answer 1

Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden and Switzerland have acceded to the Schengen Agreement and are thus Schengen states.

This means reduced border controls and an ability to stay in another Schengen country for 3 months every half year.

Answer 2

Yes you can,

You do not need a visa for short-term stays if you fall into one of the categories listed in the Temporary Stay in the Czech Republic/Schengen Area without a Visa. that is -citizens of the EU, Iceland, Norway, Liechtenstein, and Switzerland List of third countries whose citizens are exempted from visa requirement in Member States of the European Union bound by Regulation (EC) No. 539/2001, as amended by Regulation (EC) No. 2414/2001 and Regulation (EC) No. 453/2003 (i.e. in the Schengen area). Visa exemptions apply only to short stays up to 90 days of non-profit nature. If the purpose of stay is employment, Schengen (short-term) visa for the purpose of employment is required. Holders of Serbian passports issued by the Special Coordination Directorate in Belgrade are excluded from visa-free regime. In case of citizens of Serbia, Montenegro, and Macedonia/FYROM, visa-free regime applies only to holders of biometric passports.