Does IIITH release official previous year question papers?

No, despite being a "Research Aptitude" test, the computer-based format only supports objective types (MCQs) and numerical entries. There are no descriptive based questions in the IIITH UGEE exam.

The SUPR section is comparable to JEE Main, but REAP section is considered challenging as it requires creative thinking and "out-of-box" problem solving. It can be compared to the Olympiad level questions.

No, physical or on-screen calculators are strictly prohibited in both sections. 

Yes, in REAP section there can be questions on linguistics puzzles testing pattern recognition in unfamiliar languages. These questions do not require prior knowledge of the language, only logical deduction skills.

Yes, but it is lower than Physics and Mathematics. In SUPR section, the distribution is roughly 40% Mathematics, 35% Physics, and 25% Chemistry/Reasoning.