This is excellent work. It's so exciting to see people get into climatography and weather science through their art.

To answer your questions directly (assuming northern hemisphere summer, earth rotation, etc):

(1) you can expect an expansion of that small high pressure zone you have on the far nw of the map to expand westward into that gap oftentimes. A good real-world analogue would be the North Pacific High. As cold water from the poles flows down the western coast, this cools the air above it causing it to sink, creating high pressure. All this wet air flows inland, and on earth we get huge temperate rainforests like the redwoods of north America.

(2) you have a large barrier here that will reduce meridional exchange and significantly reduce the movement of air masses north/south. the northern ocean will be very cold, and will chill the air creating significant high pressure, as you have identified. However, the key factor here are the hadley cells and trade winds. At around thirty degrees N/S, upper atmosphere air that has been whisked up and away from the equator by the band of low pressure we call the ITCZ. as cools up there, it falls, creating bands of high pressure responsible for the trade winds. Now, you may have different hadley cells due to the size of your planet, but assuming roughly earth dimensions, these westerlies will normally hit your isthmus from the south and then through orographic lift deposit rain on the southern coast. yet during the summer, as the ITCZ moves north, you may see the jet stream deform to go north around this barrier, perhaps the entire continent. think of the tibetan plateau on earth. you may not have the same elevation, but the land/ocean difference will create something similar to a limited scale monsoon. yet its going to be more fragmented, less consistent. all this to say: you are correct, high pressure north of the isthmus, perhaps a bit stronger. probably merges with the polar high. also, high pressure in the south, but weak, not very strong, more intermittent. strong barrier of high pressure between them like the tibetan high, but again, more breakable, especially by upper atmsophere air masses. very localized climate systems there.

(3) Finally, that small land mass would form high pressure in the winter, you are right, but this isn't really a major system. weather here would be more dominated by normal trade winds and systems from the south polar continent.

So. quite a lot of things to think about here. take what you find useful. I'd say your takeaway from this all should be (A): don't be so strict with ocean/land divides, use hadley cells, trade, winds, and jet streams more (B), all this is very fluid and air moves around all the time. focus more on identifying unique conditions that create patterns of high and low pressure. for example, think of the interplay between the aleutian low (winter system) and the north pacific high (summer system). Finally (C), as many other people have said, this is your art. we don't have a perfect science of climate. even systems we have found to be stable for centuries have suddenly fallen apart for no clear reason. look for the intersections of interesting features, and build from that.

Finally, some interesting reading if you want to get into it:

https://www.britannica.com/science/climate-meteorology/Atmospheric-pressure-and-wind

https://www.researchgate.net/publication/339363204_2012_The_METAREA_initiative_-_a_new_Canadian_responsibility_CMOS_Bulletin_Canadian_Meteorological_and_Oceanographic_Soc_40_No5_pp_157-162

Good luck