Total Commander

Is it possible to search for certain text inside htm-files?

It depends: English text is usually no problem as long as it isn't containing any tags in the middle of the search string (e.g. for bold text). Accents and non-English characters can be a problem because if the encoding of the file (e.g. utf-8) and the characters (e.g. something like "ä").

How would I have to do that? Any special adjustments?

All you can do is look into a sample file of those you want to search and check how the text is encoded.

There is a little magnifying glass symbol,
top right corner in 'Total Commander for Android'

Tab that magnifying glass, then fill out the 'Containing text:' box.