Q. 1900's or 1900s?

I would agree with you, and so does the MLA Handbook for Writers of Research Papers, 7th edition.

This, from p. 84.

"Decades are usually written out without capitalization (the nineties), but it is acceptable to express them in figures (the 1990s, the '60s). Whichever form you use, be consistent."

The Publication Manual of the American Psychological Association, 6th edition, states this on p. 114 -

4.38 Plural of numbers
To form the plurals of numbers, whether expressed as figures or as words, add s or es alone, without an apostrophe.