ISRAELI

The scientific etymology of Israel is uncertain:
http://en.wikipedia.org/wiki/Israel_(name)

But we may easily assume the word is an adjective derived from ISR-noun.

Is the '-eli'-suffix Kartvelian? Yes, it is. You will find it, in particular, in Metreveli surname.

Is the root ISR- Kartvelian? Yes, it is. In the Kartvelian-English Dictionary you will find a word ის(ა)რი [is(a)ri] meaning 'arrow'. If you insist, that 'isri' noun should have formed ISRIEL, not ISRAEL, you should know that the name ISRAEL used to exist as ISRIEL as well:
http://boards.ancestry.com/thread.aspx?mv=flat&m=1165&p=localities.northam.usa.states.wisconsin.counties.sauk
http://boards.ancestry.ca/thread.aspx?mv=flat&m=734&p=surnames.pate
http://www.findagrave.com/cgi-bin/fg.cgi?page=fl&GSln=Bryant&GSiman=1&GScty=106342&GRid=104437066&

Do arrows characterize the Israeli people anyhow?

They do. Bows and arrows are a an integral part of Israeli Lag BaOmer holiday, when children go out to play with bows and arrows:
http://en.wikipedia.org/wiki/Lag_BaOmer#Bows_and_arrows

So, 'Israeli' means 'arrowy' from Kartvelian point of view.