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I have done a lot of these using Canadian Code. In older versions of ACI, Appendix D in ACI 318 used to cover all the limit states (mentioned by Baz above as well). I don't know what is in the latest version but you calculate your loads including moments if any, and then calculate the minimum embedment capacity for different limit states against applied loading using ACI Appendix D. If you are using Hilit, they have a free software called Profis Anchor that can do all the calculations for you. Just download and provide your rebar configurations, concrete edge distances and loads and it will calculate the embedment using Hilti Products. Thanks.

You need to follow the guidelines of chapter 17 of AC318-14/19 or equivalent sections from older versions of the same code. Assuming, you do not have tension in the column, your post installed rebars must have enough embedment to satisfy the limit states corresponding to steel failure, concrete pry out and concrete breakout failure modes.

Depends on Building Code. For some structures with irregularities response spectrum analysis is mandated by codes since equivalent static is more applicable for regular shaped buildings with continuous load path and might not give accurate seismic force distribution.

I have no doubt that you are a very competent engineer and wish you all the best but doing designs without prior experience can be dangerous! You can open a company and sublet design work to someone who is licensed and also learn from that person.