Addressing the OP's points one at a time:
1) Starting location.
Your capital needs to be near (but not *on*) a large number of river tiles, *or* a large number of fish/sea luxuries. Nothing beats an observatory so a mountain is very nice. The ideal start is coastal, adjacent to mountain, with 7+ river tiles and 4-5 fish/sea lux. On desert hills & floodplains. On gold or silver or gems. With lots of forest nearby. And salt. Or copper if nothing else. With multiple 2food1hammer tiles like grassland horses or stone. With multiple wheat tiles. Not gonna happen, but let's break it down.
For achieving the early tech lead, there are many factors. You must have good food surplus. You must have good happiness. You must have good production and gold. (To build and buy)
So, what all that is saying is: count the number of tiles that (by civil service) will generate at least 4 yield. (count 2 gold as 1 yield) Then count the total food surplus of those tiles. (ivory is -1 surplus, salt is +1, grassland is +2, fish is +3, etc.)
To achieve good food surplus, you must have many tiles of at least 3 food output. Cargo ships help a lot. Each caravan is the equivalent of 4-5 better tiles. Each cargo ship is the equivalent of 7-8 better tiles. But, nothing helps as much as a mountain though. Think of a mountain as a permanent +25%-50% growth. (Even with NC & Lab giving base 200%, +50% base is net +25%)
Gardens are fine for the late game, but they don't help you achieve the early tech lead. The first few GS would only come out a few turns early. Hanging gardens is nice if you have nothing else to build, but, don't let it distract you from science buildings and guilds. I'm not saying don't build gardens. I'm saying: If you want the early tech lead, gardens don't help. They help more the earlier you build them, so DO build them for long-term tech gains, but not for the goal you mentioned.
Also, re: settling on a lux... Do it for the ability to sell that resource early, and then get a happiness boost when the trade ends. This is *definitely* worth it.
2. Early build order
I never build workers on Deity. I steal steal steal. If you're not succeeding at this, practice it more, and be patient about stealing. Learn to recognize when to wait a turn or two. Learn to recognize better "fishing holes".
3. Trade Routes
I've gone back and forth on this, but ultimately, here's the deal. External trade routes give temporary beakers and gold. Internal trade routes give permanent hammers/beakers/gold/food. A trade route can get the ball rolling on working more 3-food tiles. (If you have the workers) This can result in a *larger surplus* than the trade route initially gave. (Each 3-food tile increases surplus by 1)
The downside is unhappiness. Early trade routes can max out your happiness quickly if you use them for growth. So, the alternative is: Use them to work more mines and pump out buildings while still growing at a balanced rate. I look at my happiness situation (unique luxuries, available workers, turns until a tile is workable) and choose internal/external based on this.
4. National college
Consider building NC after building a settler but before planting it. Or build settlers in your expo while building NC. Either way, planting 2 settlers *right after* you finish NC will result in a 4-city NC built faster. That's one option. The two options I prefer are 1) early gold deals so I can buy the library in my 4th city. 2) 3-city NC.
Chopping forest helps a lot here. I save forest for NC instead of using it on settlers/libraries/wonders in the capital. If you get an early snowball going, early NC is not hard. So focus on getting that early snowball. A rush-bought caravan will often yield more than a rush-bought library. There are many factors. Look at your situation and adjust. Growing fast? Ally a mercantile CS. The snowball is the key to an early NC. Sometimes a rush-bought granary in an expo is worth it, to get a TR going to the capital. That's another advantage of external trade routes though... not having to build granaries to use them... but delaying granaries has negative side effects.
5. Tradition or Liberty?
If you want to overtake the AI early tech-wise, Tradition Tradition Tradition. No question.
6. Managing early war
Early war does not play nice with getting an early tech lead. My advice? Don't do it. Unless your definition of early extends to t170-200.
Don't skip out on markets. They come in handy for Secularism anyway. Send more food to the capital. (More money)
Don't build anything you don't need. It all costs money. For peaceful play, a minimal defense force garrisoned is free. This makes a big difference.
8. Hard building or buying the key buildings
It is always possible to save up enough money to rush-buy at least 2 universities. Whenever you're about to spend a few hundred gold, ask yourself if getting X a few turns earlier is better than getting universities ASAP. The answer is usually, but not always, no! Rush-buy universities in big cities, not small ones. It's counter-intuitive, in the sense that small cities take forever to build them, and big ones build them fast. But, big cities can actually afford to stock specialists, and provide more science yield from that +33%. Also, on that note, *no city* should be small or have poor production by now. Workers! Trade routes! Farms! Every city should be capable of building a university in 12 turns by the time you get the tech. Consider also that in peaceful play, rush-buying 4 universities is feasible. 2600 gold can be saved up by t100 if you never buy anything else except archer upgrades. 3 is more reasonable though.
9. Religion and culture
Temples are a waste. Guilds go in the city with the best food surplus unless another city will run out of good tiles first. (Avoid unemployed citizens)
Cultural CS allies are critical. For early tech lead, Free Thought is overkill. You *should* have the tech lead after Secularism if you've been playing your cards right. If not, push for Free Thought, but you won't get it until World's Fair unless you're Poland or have multiple CS allies. Most games that's not until t160.
World's Fair is essential. Save up those GW. If you don't have the tech lead by t160, Free Thought should do it.
But again, this is for peaceful play. Warmongering while going for the tech lead is extremely tough.
10. Social policies up from the opening tree
Tradition->Rationalism. Earlier Education gets you earlier Rationalism. CS allies before Education will force you to spend a point in Commerce or something though. That's fine, but CS allies + guilds will result in 2 points in Commerce and delayed Rationalism. Which is ALSO fine, IF the reason Rationalism was delayed was that you got so many policies so quick. It also means you got early aqueducts and are kicking ass in general.
11. Great Scientists - planting, bulbing or saving - quite simply, what's your view?
Plant 1-2, save the rest, for peaceful play.
12. When to do the Oxford Uni?
Oxford for Plastics, Radio or Scientific Theory. Lots of ways to skin this cat. The earlier you use it, the less benefit, but the more snowball you get. Don't bulb Sci Theory or Plastics if you don't have gold/production to spend. Busy doing the World's Fair? No point in bulbing Plastics. etc.
13. When do you start working your specialist slots and with what priority?
Universities, ASAP! Markets at Secularism. Workshops ASAP after that.