I’m getting the hang of micromanaging my cities, tracking points-per-turn and assigning citizens to tiles. My question is this; when I’m in the City Screen, how do I assign a citizen (not a Citizen/Priest/Artist etc.) to a work tile outside of the City Screen square? I can’t just click on it because the other City Screen components are it the way.
You can't use those tiles with that city. Tiles need to be within the Big Fat Cross (BFC) of a city in order to be workable by that city. This is the area that you see after the first border expansion of the city, it contain 21 tiles. It's a square area of 5x5 without the four corners.
Do you expect to have all the techs? The few times I’ve won, on Chieftain Level, have been Time victories and I’ve only gotten as far as the Plastics and Ecology techs and that’s without getting every single tech along the way. I’ve read here about the UN and the Space Race and haven’t gotten even remotely close before I run out of Turns. What am I doing wrong or is it the difficulty level I’m on?
Yes, it's very possible to research the entire technology tree before the natural end date of the game. Experienced players do it even far earlier. Technology trading allows players to research quicker on the higher difficulty levels as their trading partners are likely more advanced than on the lower levels and thus better trading partners. This way, researching a single technology can through trading give them 3 or 4 technologies. But technology trading is only a small part of the reason why experienced players research quicker. I for instance always play without technology trading and still are far ahead of the historical dates of technology advances.
You're rather inexperienced with this game I guess since you're still playing on chieftain level. There are likely lots of things in your game strategy that can be improved. Don't worry about it, you'll get there with some more experience. You can read some of the
War Academy articles to learn from the tactics and strategy of others.
Things that you can likely improve include:
-Learn that you gain research points mainly through commerce and some specialists (such as scientists). Commerce mainly originates from cottages, some special tiles and trade, especially foreign trade routes.
-Learn that the research rate is in no way related to the percentage that you invest in technology. This is somehow a thought that prevails on this site while it is utterly false. The rate of technology research is almost purely related to the amount of research points you earn each turn which can be viewed in the financial advisor. So don't for instance limit your expansion just to keep the research percentage at 80% or higher.
-Learn how to improve the terrain around a city in such a way as to optimise its output. There's a lot that can be said about this.
-Learn that some buildings in some cities only offer minor benefits and thus other build orders might be more beneficial. You don't need to build everything in every city.
-Related to the above two issues is is city specialisation where some cities focus on specific terrain improvement and combine this with buildings which enhance the output of these terrain improvements. You can think in terms of research, gold, production and great person cities. This works by far best when used with the special national wonders.
-Learn that a larger empire researches quicker. This isn't completely true for an early game empire which consists of barely improved tiny cities as the upkeep cost are to high for such low output cities. However, it is true once these cities start growing and gaining some more improvements.
-Learn that it's better to trade one technology with 3 neighbours in return for one of theirs. You gain three technologies, they gain one each.
And people say that Vassalage is broken! 
All this in patched BtS, at least...
