For history and walking, consider north Wales. Castles: Conwy, Caernarvon, Beaumaris and others are all accessible by public transport. Walking: Snowdonia National Park and Conwy Valley. Lots of other choices available.

If you want to move from park to park by yourselves,either self driving or using public transport, then it is probably easier to do in Kenya than Tanzania.
You can just turn up, pay the entrance fee (in cash dollars) and go in. Tanzania has quite complicated rules about payment.

Exactly, it may be the only way to reach an area.
There's no public transportation in many places (like the Scottish highlands), or they're so irregular as to be unusable when you have only a few days to spend in a region. And places like Guna Yala islands are only reachable by motorboats and controlled entirely by the indigenous population.

but will there be any problems with public transport to Rio from other towns & cities during Carnival?

Public transport and intercity transport usually run as normal.

There are lots of popular blocos like Sarmiento Pimenta, Banda de Ipanema, Cordão do Bola Preta, Simpatia é Quase Amor, Céu na Terra, Carmelitas, Que Merda é Essa, etc etc... Best is to ask a local about what ones are best if you can. Your accom will have some suggestions.

...like here to get individuals' personal impressions...

I'm local, not an american who traveled to the Baltics. Reading your posts i got some contradicting and mixed impressions about your opinion of your future trip. It reads in your profile: "...I admit to being a country counter....", so what's a problem with getting Belarus visa - you get the visa, enter the country, and have one more country in your list. And on your passport. And with a proper visa you can proceed your trip from Belarus any direction, eg to Moscow. You originally didn't intend to visit Belarus, but why do you intend to go to Moscow necessarily from Lithuania?

I'm not against "counting the countries", it's just unusual to read about wide interests of the same person. Either you don't have enough time to satisfy your interests, or the number countries will be fewer. Which one is a priority?

What are the must sees and dos?

The Baltics themselves are neither must sees nor dos. Especially for the person who over the last 41 years have visited over 90 nations - what "adventure & unique experiences" do you expect? Well, there may be some, but you already stressed your rich experience in travels and didn't specify what is, say, "rough idea" or "image" of your trip. Not countries, but your trip. It looks as if you expect to receive the very expert advice, while you yourself are the decent expert in many spheres (given your experience of travels and knowing languages). To me your questions seems rather useless because they look like the questions of a person who is lazy to read the basic info in some basic guidebook. Well, if you've posted some expert question (except that one re visas for americans) it could be difficult to answer, maybe, but it at least would be interesting and worth the challenge.

Regarding transportation. Public transport is good (in local sense), renting a car is recommended for persons who have wide (or just particular) interests, this also is the way that locals do, and not recommended if timeframe is very tight and/or priority is the counting, so to say. To me this all seems quite contradicting situation in everything. And good opportunity to post my reasoning... LOL... Sorry.

What come to mind, having all your questions in mind as a whole one, - get a car, get a list of observation towers and visit them purposefully. You automatically will have the routes and roads ready in your navigation system, or on your print map, or written on the separate list (up to you), you automatically will visit most attractive or picturesque spots of the country (including some in recreation or protected areas), while areas in between will be a "daily-life-thing", and you will be able to check some "alone standing" objects that are scattered everywhere and are always skipped if traveling by public transport. Organizing and implementing that all can count as adventure. Can't say what would be unique, though...

I have visited Tizimin, which is about halfway from Valladolid to Rio Lagartos, by second class bus, and I'm sure there is some kind of public transport to take you the rest of the way. Have you checked Yucatan Today for schedules?