Can someone explain the differences between "neta", "preciza" etc?
Also, can I translate English "precisely" by one of those words with "e" instead of "a"/"an"/"aj"/"ajn"?

1) Neta means netto; raw text (?, English is not my native language).

Ekzemploj:

• neta salajro : net salary, i.e. salary after all taxes, social security fees etc.
  
• neta profito : net profit, i.e. what remains after all costs have been deducted
  
• neta kopio : raw copy, i.e. complete text before any proof-reading and corrections of typos etc.

I admit, that I had to check at PIV for other meanings besides the obvious one, neta salajro.

2) I'm not sure, that I understand your question.

The adverb "precisely" is precize and the corresponding adjective preciza.

Ajn is a particle, that explicitly denotes indifference, randomness.

Ekzemploj:

• Kiu ajn tion diris al vi… : Whatever that says to you…
  
• Kiam ajn vi venos… : Whenever you will come…
  
• Faru iun ajn decidon! : Make some decision/Make up your mind!

There is a corresponding adjective ajna:
ajna nombro : a random number

Do NOT use ajn in a negation like in English (not + any).

I don't have any book(s) : (wrong!) *Mi ne havas ajn libro(j)n*; (correct) Mi havas neniun libron