Re Re card counting: The vast, vast majority of advantage when counting is the choice to change your bet size depending on the count. When a deck starts you are at some initial count and then it goes up or down as the deck goes along. While the count is at or below a certain point (low counts are considered bad and high counts are considered good), you usually just bet the table minimum as you do not have an advantage over the house. Once the count reaches a certain level you start betting more aggresively. There is usually a spread to counts where for example if the count is 1 you bet 2x table minimum if it is 3 you bet 4x table minimum etc. This is how you take advantage of the fact that the odds are in your favor - if you just bet the same amount all the time you are not really doing anything different (assuming you are following Basic Strategy at all times).
The rub here is that this type of betting can be seen by the house. If you are of enough interest to the casino (something you can get playing $100 hands let along $100K hands) they will watch you bet and try and look for this pattern. Most casinos employ former counters or have people on staff you can, after a little bit of time, determine if you are counting or not and politely ask you to leave. In fact most counters will specifically give away some of their advantage by going against the recommended bet at a given count to try and make it look less like they are counting. One such practice would be to never go from a minimum bet to a max bet, as it is most likely not something a regular counter would do (aka bet $100 one hand then bet $1K the next hand).
You are correct however that some advantage can be gained by just "tracking whether you've seen a lot of high cards". Players use indexes which will change their play depending on the count, and use this skill to augment their changes in betting amounts to better take advantage of their current position. You can see the effect of using indexes vs. no indexes here: https://www.qfit.com/cardcountingindexes.htm
The rub here is that this type of betting can be seen by the house. If you are of enough interest to the casino (something you can get playing $100 hands let along $100K hands) they will watch you bet and try and look for this pattern. Most casinos employ former counters or have people on staff you can, after a little bit of time, determine if you are counting or not and politely ask you to leave. In fact most counters will specifically give away some of their advantage by going against the recommended bet at a given count to try and make it look less like they are counting. One such practice would be to never go from a minimum bet to a max bet, as it is most likely not something a regular counter would do (aka bet $100 one hand then bet $1K the next hand).
You are correct however that some advantage can be gained by just "tracking whether you've seen a lot of high cards". Players use indexes which will change their play depending on the count, and use this skill to augment their changes in betting amounts to better take advantage of their current position. You can see the effect of using indexes vs. no indexes here: https://www.qfit.com/cardcountingindexes.htm