Could someone share some personal impressions, to help me understand the key points of the Every Student Succeeds Act (ESSA)? And, how does it relate to the four groups in education known as English Language Learners (ELL), Learning Disabled Learners (LDL), Advanced Learners (AL), and Economically Disadvantaged Learners (EDL)?

A key feature to the Every Student Succeeds Act is that it gives individual states new flexibility on how to exactly improve education in various districts.  For example, states can pick which long term and short term goals to work on; however, the goals need to address test proficiency, English language proficiency, and graduation rates.  The focus is to require that "all students in America be taught to high academic standards that will prepare them to succeed in college and careers." 
Another key point of the Every Student Succeeds Act is that it increases focus on lower performing schools.  States are required to "identify and intervene" in a high school that has a graduation rate of 67% or lower.  What's good about the focus is that the ESSA allows individual school districts to figure out and implement a plan to help the struggling schools.  States will monitor the progress of the school, and if no improvements are made, the state can take over the school to implement its own plan. 
Standards based education is still a priority with the ESSA in that states are required to adopt "challenging" academic standards; however, individual states are free to pick their own set of standards.  In fact, the ESSA expressly prohibits the Secretary of Education from even encouraging a state to pick one set of standards over another. For example, no state would be required to adopt the Common Core State Standards.  
The ESSA has an increased focus on English Language Learners.  This is evidenced by the fact that ELLs' accountability has been moved from Title III to Title I. By a student's third year in the country, his/her test scores are treated no differently than any other student's test scores. 
As for students with learning disabilities, the ESSA maintains its focus on high standards.  Only 1% of students (overall) are going to be allowed to take alternative tests.  A consequence of this 1% cap is that the testing needs of many students with learning disabilities could be ignored. 
Regarding Advanced Learners and Economically Disadvantaged Learners, a provision in the ESSA allows states to use up to 3% of their Title I money to create new programs.  The aim is for money to go to schools and districts in lower income areas, which should help those students reach higher levels of achievement.  Some of those students are likely Advanced Learners; therefore, the ESSA is attempting to spread funding around so that more students can be Advanced Learners.  Michael Magee, the CEO of Chiefs for Change, says the following about the ESSA.

 ". . . it will help a great many schools create new tutoring programs or Advanced Placement classes, or devise new ways to use technology."
https://educationpost.org/this-little-provision-of-essa-could-make-a-big-difference-for-low-income-kids/