Yes, these were formerly quite common. And as you suspect, have largely fallen out of use.

The two dots in this instance are called diaeresis. The mark always occurs with two vowels next to each other, and shows up above the second vowel. It signifies that the two vowels are each holding their own syllable / are not a glide. A common example of an English word which still gets it quite often is "naïve". The diaeresis tells us it's not pronounced like "knives" minus the s. Another common example is "coöperate" (not coo-perate). It's also not uncommon to see words split with a hyphen to mark the same thing, e.g. "co-operate".

English has never been much for diacritics (marks above/below/through letters) like façade, résumé etc. We don't have a habit of typing these and we're just as comfortable with ignoring them completely.

Ligatures (the connection of two letters into a single glyph) used to also be more common. In fact, you could say they were rampant. The short history is that, back in the days of Gutenberg-style printing presses, ligatures were incredibly useful as far as speeding up the physical act of typesetting a printed work. It was very costly to go through and place each letter by hand, so for the most common of these, ligatures were a great help. It wasn't just <æ> either. There's also <œ>, things like <ȣ> for <ou>, a connected <ij> (won't show as on your end as connected, depending on your fonts), plus a ligature which has now become a full letter in its own right, German's <ß> (a combination of <ſ> (the archaic long s) and <s> (ſs = ß), and, actually, <&>, which is itself just a stylised "et" (Latin for "and"). The most common today at least that I encounter is <fi>, which my iPhone is a pretty big fan of. If you look closely, there's a good chance you'll see a lot of connected <fi> glyphs.

This gets us to the question of why they fell out of fashion. In part, typewriters are to blame. As printing stopped being the domain of those with large printing presses and became something people could do at home, ligatures stopped being required or even convenient. Various shifts in style among publishers also had a role to play, in the same way that such shifts influenced English spelling.

Today, it's more trouble to write "encyclopædia" or "anæsthesia" or "diarrhœæ" or "manœuvre" with the ligatures than without. The average computer user won't know how to type those letters, and if you use them, it's going to look intentionally archaic, and your spell-checker is just going to scold you about them anyway.

No, it is not unusual to encounter spellings like coöperate, naïve, mediæval, and rôle in books of this age.

They haven't entirely disappeared, either. The New Yorker notably continues to use a diaeresis in words like coöperate and reëlect as a policy of in-house style. In 1978, Hobie Weeks, an editor who had been at the magazine for fifty years, let it be known that he was on the verge of changing that style, already seen at that time as obsolete, and would be sending out a memo soon. Then he died.