I think you are okay. I like the way you have picked an eclectic list of sites that are important to you. It is great when people really personalize their vacations.

The best answer I can give you on your transportation questions is to use the free CityMapper app. Good for major cities around the world, it especially effective in London. It will plan routes and give you realtime information.

I think you have a good pace. You can always add an Uber or cab if you're short on time or energy.

I also think you have a good list and plan that you obviously considered for what you like/want to see. For me, I would skip Tate Modern and visit the National Gallery instead, but that depends on what kind or era of art you prefer. I've been to London a number of times, and have mostly stayed in Bloomsbury.

I love walking in cities; there's so much to see! On my last year's visit to London, I walked from my small hotel near Victoria Station all the way to the City, and enjoyed every minute.

You will LOVE Dennis Severs house. If you want to visit something else that's a bit similar, in terms of being what I call a "house museum," and in the Bloomsbury, consider Sir John Soanes' (house) Museum.

If you have a data plan on your phone, it's easy to use Google Maps to decide on your best public transportation route, if you get tired of walking. The Tube is a great thing, but keep in mind sometimes it's faster to walk, depending on the lines you would have to take.

I think this sounds like a very nice trip and it's not too much. To answer some of your questions:

-To get to Leake Street arches, I would walk to Tottenham Court Road (on the edge of Bloomsbury) and get the Northern Line to Waterloo.
-To get from St Paul's back to Bloomsbury, you can just get the Central Line two stops to Holborn.
-To get from Bloomsbury to Tower of London I would probably get the Central line from Holborn to Liverpool Street and then change to the Circle Line to Tower Hill. Or if you're not staying that far from Kings Cross just walk there and get the Circle Line.
-Others may recommend buses, and these are also fine. But I personally hate sitting in traffic on a bus and will always take the tube over a bus, even if it means changes.
-For the same reason (traffic) I also very rarely take taxis- pretty much only if I have a very early flight. You could take a taxi between any of these for the experience, but just be prepared to sit in some traffic.
-If you want to save some money, you can take the Elizabeth Line to the airport (your closest top will be Tottenham Court Road).

Good luck with your planning!

Use the Citymapper app to plan your journeys and to help you when you are out and about. It links to the ‘live’ Transport for London (TFL) data so is reliable and easy to use.

Preferences when using public transport are personal and generally there are few rights and wrongs.
For short trips I prefer the bus. Even factoring in how slow the traffic can be once you include how long it can take to navigate to and from platforms in tube stations it isn’t necessarily slower. Buses also have the advantage that if there is a problem you can just get off and walk. Problems on the tube, you can be a bit stuck. On the bus you also get to enjoy the sights. For example, there is so much variety in building styles to enjoy if you just look up when travelling on the bus.