Once the sefer Torah is opened you may not exit even if you already heard krias haTorah. (ShA2 – MB1)
You can go out between aliyos only under all of the following conditions:
A minyan is left in shul.
Important need.
You already heard krias haTorah or you will come right back.
Only once in a while (ShA1 – MB2,3 – BeH “oval”)
Once the sefer Torah is opened you may not talk even divray Torah. (ShA2)
Exception: stopping someone from a transgression (if they do not get a hint). (MB5)
Between aliyos you may learn Torah to yourself and tell over a p’sak halacha to someone. Besides that, don’t talk even if you already heard krias haTorah. (MB6,7 – ShaH9)
To go over shnayim mikra v’echad targum during krias haTorah is permitted since it’s the same topic. Do it quietly but you don’t need to be at the same possuk as the baal koray. (ShA2 – MB11)
The best practice is to direct your thoughts and listen to the parsha that is being read. It is proper to read along quietly to aid your concentration . (ShA2 –MB15)
It is forbidden to speak while the maftir is reading the navi just like krias haTorah. Pay attention to his berachos and answer omayn after them. (ShA3 – MB16)
You do not have to stand during krias haTorah even though you are within 4 amos of the bima. But when Borchu is said and when responding “Boruch Hashem ham’vorach…”, you must stand – it’s a dovar shebikdusha. (ShA4 – MB18)
When they carry the sefer Torah you are required to stand until it is either out of view, or it has come to its resting place. During this time, do not even lean on something. (MB17)
Some people are machmir to stand for krias haTorah, having an image of receiving the Torah on har Sinai in their minds. Do not stand if you are weak and it will disturb your concentration. (Rama4 – MB19)
Even those who stand for krias haTorah can sit between aliyos. (MB20)