If you are trying to learn to beat Deity reliably definitely always choose standard/pangaea. It makes loads of things easier. You should see a theme here. Close neighbors make Deity games actually way easier in some ways. A close peaceful neighbor will give up 2 easy early workers to steals. Make peace with you, and then you can trade trade routes for tons of early science and gold. It can take dozens of turns off your early game. I presume this is why a lot of players like standard or small pangaea because it makes this setup more likely. If your close neighbor is a warmonger that is unlikely to peace out if attacked, skip him and look for the next closest, them start bribing him to war others with your first lux or resources. Sometimes you can get away with stealing an honor/warmongers workers but they are far less likely to forgive since they have larger earlier armies. By the time you'd be peacing out they will already have a decent force and might decide to just come after you, so stealing from them is not a sure think like it is from normal AI which are likely to just peace out in 10 turns for white peace and won't come after you for a while even if you stay at war.
1. The best starting tiles to work are the 2f1h or 3f ones. If I have the option to work a 2f1h tile or a low-production 3f one I usually start with the 3f one for a few turns then switch to the 2f1h one. This kind of micro gets you growth in 5-6 turns but still is enough to reduce the time on the scout so you get both. If you start on a hill the scout 5 turns rather then 7 turns no matter which you work due to the extra hill hammer and it's why everyone loves hills. In general, right after you grow, work high food tiles to reduce the growth time to the next. When you get within 1-3 turns of growth you can micro your tiles to still grow at the same time but bring in more gold, hammers, or faith in the last few turns. And then, obviously check production focus as many players advise so you get 1-2 extra hammers on the growth turn.
2. I always farm riverside hills for the most part. In the beginning you can't afford to work straight mines except when building settlers. So most of the game the farmed hill or sheep hills, stone quarries, deer, horses, iron/grass, etc. are a great compromise to still grow well but also add extra hammers into your pool. These things make a much bigger difference for starts with poor production, your start is very strong in hammers due to the large amount of choppable forests, plains under your growth tiles, salt, riverside hills, etc, so you want to squeeze all the food you can out of it. You'll get the hammers naturally.
3. Stealing workers from AI on immortal and Deity is a bit of an art. Especially because there often hidden warriors circling the city that could kill you that you can't see until you steal. Often waiting a few turns to scout the border or sitting on a hill and locating these warriors and stealing at the proper time can save you from losing it again. If you have been following the game with 4 starts I successfully stole workers with 3/4 civs and lost with one. I explain why it happened and what you can do to reduce the chance. Stealing from city states is a great fallback but they don't produce them till later so you'll get it and be back at your closest city no early then turn 30. By this time usually you could have built your own so one conservative strategy if you aren't comfortable stealing from the AI is to start building an early worker, steal from CS, then you have 2 around turn 30, one to chop to speed settlers and one to improve and hook up resources and luxuries. Pick a CS near you and stay at war to steal 1-2 more. vids of people stealing workers before turn 10 REQUIRES close neighbors, so it's not a hallmark of successful strategy but entirely luck. You happened to explore the right direction and find a civ and locate the worker and be able to steal it right away without getting pwned by the 2-3 warriors usually guarding it (aka flatland without bad river placement). Often if you rush in to steal with your warrior as soon as you see the worker you'll just die, especially if the spot is adjacent to the city. One bombard, 2 warrior attacks and you're down in red. Sometimes a warriors ZOC prevents you from getting away with forest/hill terrain. This is why stealing on first sight without a spearman upgrade is actually very risky. It's much better to hang around a couple turns and scout to make sure you can do it and get away. A super-early worker makes less of a difference then you think if you don't have the techs to use it. The guy that opens with mining first probably plays map settings that make it pretty likely to have close AI neighbors for stealing, maybe small/pangaea. On the large/huge maps I've played you can hike for 20 turns before locating someone making mining a very poor early choice. Remember you also have to hike back after stealing so even if you do steal by turn 10 you gotta bring that guy back. By turn 17-18 you have your 2nd tech and 23-24 your 3rd given you had ok growth so mining 2nd or 3rd is actually what I prefer for random unknown map settings. It depends very heavily on your starting map conditions what techs you go for.
4. With that start I would have gone pottery --> mining --> animal husbandry. Mining is useless till you get your first worker and even with an early steal I'm betting you won't get him back until after 18 turns at which point you'll have mining. It's useless until you steal AND get him back in territory. Why do I choose pottery over animal husbandry? You have 3 tiles buffable by the granary for a total of 5 extra early food. Though it's true you won't be building the granary in the first 18 turns you definitely probably want mining 2nd with that start of salt and forest and should be looking for a worker to steal ASAP and pottery 3rd would be too long to wait. Also opening pottery early gives you the option for a pantheon if as you explore you see a good one, and opening pottery gives you a much higher chance of the free techs from ruins being a tier-2 ones since it reveals 3 new tier-2 techs. Sometimes this choice means a free early writing, calendar, or sailing! Animal Husbandry shows horses. There's maybe a 50% chance you have one unless you played strategic balance. You already have 4 hammer and food balanced tiles to work though and another one is useless till you get to population 5 which will be a long time. Animal Husbandry is a solid opener if you start looks poor, esp. hammer poor grassland, as the appearance of 1-2 horse tiles can really help out. Even if you have horses you need to hook them up to use them for early gold and your worker already has salt to, wheat to farm, and several forest to clear. 3rd will be fine, and then you have the option to put a few hammers into a caravan between settlers if you have a close enough neighbor.
5. Shrine is your call. If you don't go for it then mining --> pottery --> animal husbandry is also fine order, but in general pottery is superior. It's unlikely you'd have a worker stolen and back in before turn 18 without tons of luck or can guarantee a close locateable neighbor with consistent map settings, and usually the luck favors the pottery choice more often with random map conditions. I'd go pottery and as you scout you'll soon know if a pantheon is a solid choice. On deity you'll found late so keep in mind even your 2nd city will be up by the time you found usually. So if nearby areas are great for a pantheon as well that works too.
6. Don't hike your warrior through the rough like that. You need him to speed over to the closest civ once you locate it. However, that spearman upgrade is great. I know that culture and growth are considered better for timing, but having a spearman means you've got a guaranteed worker steal. If you get over to Babylon quickly enough they can't kill him before he steals and gets away. It makes stealing workers easy and repeatable. Do it once, hang around to heal, and do it again and you'll get both of his Deity workers. Camp near a site he wants to improve.
7. Culture ruins: you had some sarcastic comments about them. Yes, they are luck, however, there is some math too. Each time you nab a ruin it ISN'T random what you get. Only the first one is random. Then the same ruin find can't reoccur for several others. This means the more ruins you get in a short time the higher the chance you get the ones you want like culture or growth. So efficient exploration can make it far more likely. I am not good at efficient exploration as you pointed out, and it's something that I have to work on as well, but understanding this math can help you in your quest to be better. So if you know there are lots for ruins (pangaea) more scouts greatly improve your probability to get the nice ones. Make at least 2 as you have done to maximize this chance.