> that can be deployed over a cheap hardware like RPi, or an old android phone.
Power usage will dominate hardware costs, making that hardware expensive, not cheap, probably more expensive than hardware designed to run 24/7 in a data center.
> build a search engine like Google (including in terms of quality, reliability and following web standards).
You won’t get reliability from “an old android phone”
> what challenges I may face since starting or deploying in production.
Buy a napkin first, and use it to make some calculations. Starting numbers: according to https://blog.hubspot.com/marketing/google-search-statistics, Google handles about 250k queries per second. https://zyppy.com/seo/google-index-size/ They have an index with 400 billion documents.