Could you direct me to any of your videos or books that may have dealt with these questions before?

I recommend this playlist – https://www.youtube.com/watch?v=wpgsAO-sEyM&list=PLqnDwobT_2hDgtakRqjsOy1IwaHArs4t8 – because I think it shows how simple but perfect all the fundamental pieces of astrology are.

Does the tropical zodiac work with what the sky looks like right now? 

It doesn’t. It works with the segments the sun traverses over the course of a year, relative to its highest and lowest points. 

The size of the segments is determined by the period of the lunar orbit. 

The playlist I linked above explain this in a clear, visual way.

Did the Indians decide to use the Ayanamsha to backtrack and make it so that the chart would be as if the precession of the axes did not happen? 

About 2k years ago people all over the world, including Indians, translated the solstices and equinoxes to the stars that were near them, so they could visually verify their zodiacal calculations. 

Hipparchus noticed and declared that this technique was dicey, because the relationship between solstice and star changes gradually due to axial precession. Within a relatively short time after this, practically the entire world abandoned the idea of making any permanent correlation between stars and signs. (i.e. they abandoned the concept of a “sidereal zodiac”).

India alone did not. It is not clear why, especially when the sanskrit textbooks are perfectly clear that the zodiac is tropical (based on solstices), not sidereal (based on stars) – for more on this, please see http://vicdicara.com/tropical.

Perhaps this happened due to the dominance of tradition-patterns in Indian culture; once a thing starts being done in a certain way, it is very difficult to change it? Perhaps it had to do with the fact that their stellar astrology was much more fully developed than most of the rest of the world, so they had a strong bias to make it cleanly and permanently aligned with the newly emerging systems of zodiacal calculations? I don’t know.

How does it make sense to apply the Ayanamsha to the ascendant? Isn’t the ascendant not a star, and just the actual horizon? 

The ascendant is not a star, it is the eastern horizon – but if you want to know which stars are rising on the eastern horizon, you need to know star positions relative to the sun, which means you need a way to convert from solstice/tropical to sidereal/stellar measurements.

Does this not disprove the theory of cosmic rays from the stars influencing fate that was put forward by Ptolemy and others?

Ptolemy had a very bad theory. Just because his name was Ptolemy doesn’t exempt him from having really bad ideas sometimes. For more on this, please see: https://youtu.be/7Tw0RlARYtM

How can a person have Aries ascendant characteristics now, 2k years ago, and also in Vedic times – when revati is in Aries now, Ashwini 2k years ago, and Krittika in Vedic times?

Astrological interpretation is all about how symbols overlay and intermix with each other. We would chuckle if someone complained, “I know what a sign symbolizes, and I know what a house symbolizes – but it is crazy to ask me to consider that any sign could be in any house.”

That sort of complaint is not different from saying, “I know what a nakshatra symbolizes, and I know what a sign symbolizes – but it is crazy to ask me to consider that any nakshatra could be in any sign.”

The main difference between the two situations is only that signs rotate through all the houses once per 24 hours, while nakshatras rotate through all the signs once per c. 24 thousand years.

At certain points in history there can be various ideal or anti-ideal overlays of nakshatra and rashi, just like there are ideal and non-ideal overlays of signs and houses. But the nakshatra-rashi mixtures last a lot longer and therefore describe very long term cultural developments in humanity. For example, as revati slowly drifts through Aries it is anti-ideal for what Revati represents (Parenting, mostly). At other times in history, when Revati drifts through Pisces or Taurus, we should expect better family units in general during those periods of time.