Thank you for your kind words. :))

If I'm not wrong, our adaptive immune system is always activated when our innate immune system (e.g., dendritic cells) recognize a foreign invader and then alert the adaptive immune system. But how effective is the adaptive immune system is a different matter. Older age and medical comorbidities, for examples, are known to weaken the adaptive immunity. Thus, viruses may survive and overcome the adaptive immunity.

Yes, the current mRNA vaccine for Covid-19 does activate T-cells, which are part of the adaptive immunity. Our innate immunity is the first line of defense, so they are usually activated quickly upon encounter with a foreign invader. So, vaccines aim to train the adaptive immune system's memory so that it can become activated faster the next time it sees the foreign invader. Without vaccines, the adaptive immunity would take up to a week or more to respond.

Since mRNA based vaccines are new, I don't think (at least I've not seen) data comparing efficacy between different vaccine types. And yes, mRNA vaccines can be re-designed relatively quickly than traditional vaccines. All it needs is the genetic code of the new SARS-CoV-2 variant/strain that might evade current vaccines in the future.

About half-dose vaccines, I'm not sure if there's any data supporting its efficacy. But as you have pointed out, it might lead to vaccine resistance in a similar manner as incomplete antibiotics intake resulting in antibiotic resistance.