It seems to me that you are having trouble understanding the rhythmic aspects of the score. What you highlighted is simply just dots and beamed rhythms. I'll point out some of the basics that are tripping you up here, but if you are having trouble with this you should really take a step back and learn the basics first.
The dot adds half of the value of the note to itself so a dotted quarter note take up the length of a quarter note and an eighth note. Like so:
The beams are just like the flags for eighth notes and lower. One beam is the same as one flag which corresponds to an eighth notes. See the chart below for examples up to 64th notes:
What you're looking at is an attempt to notate a relaxed style of performance where notes don't come strictly on the beat. It looks complex, is actually very natural. I'm not sure that a rigid approach to counting these rhythms out will be much use to you. It's more a matter of recognising that 'stand' is on the first beat of bar 2, but 'laid back' a bit. Hard to explain, easy to demonstrate. Can you find someone to do so?