Stockholm

We will arrive in Stockholm via the Tallink Silja overnight ferry from
Tallinn; boat docks at 10am. Hoping to take public
transportation/metro to the city center (we are comfortable using
metro systems; our hotel is near the train station). I found
information (Seat61.com) for going from the train station to the
ferry. We had assumed we would just reverse those directions - walk 12
minutes to Gardet Station, then 3 stops to T-Centralen.

That is exactly what you do. There is some construction in the area, but it is not that confusing in my opinion. (Although I haven't done it myself recently.) There is a walkway from the terminal that you just follow. It ends in a small street in a park, you follow the street through the park and arrive at a larger street. Cross that street, turn right, take the next street to the left and you see the metro station on the right. Just follow the "Tunnelbana" and "Gärdet" signs. And while staying close to the central station has its advantages, it is in general not an area I recommend staying in.

Can you see the “metro station art” without buying a ticket to ride?
We thought the blue line at stations T-Centralen and Kungsträdgården
looked interesting.

Not really, most of it is behind the ticket barriers.

I don’t like tight spaces; ok with lots of steps. Should we attempt
the City Hall Tower climb?

Maybe, there are some tight spaces when going up to the tower. If they are too tight for you is hard for me to say, but my spontaneous thought is that there maybe it's not the best for you.

Is the Katarina Observation Deck worthwhile?

Do you mean Katarinahissen (The Katarina lift)? It certainly gives you some nice views of the city.

Thoughts on the Arrurat Beer Hall? Other better dinner options that
would please a beer lover?

Never heard of that and Google doesn't give me any answers, so you probably need to check the spelling. But yes, it's safe to walk in Stockholm. Any reason why it wouldn't be? But the metro is also a good option if you want to go somewhere else, the metro runs 24h/day during weekends. I do not recommend using Uber.

Maybe Arrurat should read Akkurat, just from using the Bing search engine?

Thanks for replies.
Yes, should have read Akkurat (gotta love auto correct).

We selected Frey’s Hotel from Rick’s recommendations specifically because it’s close to train station - we have to catch a 8:20am train.

There is an observation deck where the Katarina lift ends, you can reach it from Urvädersgränd/Mosebacke torg without taking the lift. Fjällgatan and Monteliusvägen are also famous for views.

Akkurat is good and will fit the bill for beer lovers. I can also recommend Kvarnen (historic beer hall near Medborgarplatsen metro station, good Swedish classics, check out their lunch deals) or Zum Franziskaner (German style with hearty Germanic/Swedish dishes, a historic and cozy place in Gamla Stan). Both of those have a nice atmosphere, decent food and good beer.

Akkurat makes more sense, and it's not a bad idea. Zum Franziskaner should also be on the list. Other options are Katarina Ölcafé, Fjäderholmarnas bryggeri, Münchenbryggeriet, Internationella Pressklubben, Babajan, Omnipollos hatt or Omaka.

Again, many thanks to everyone who replied.

Badger, special thanks for detailed description of route to metro station.

Don't mention it. In hindsight I think my description was a bit too detailed, the short version is: Follow the crowd, you will not be the only one heading to the metro.