The SOA and NS records are critical for the functioning of a DNS zone.
The SOA record contains some timeouts (you can use the defaults as listed in the example), it contains a email address in case somebody wants to contact the administrator of the zone. You can put any of your e-mails there, by default an email like hostmaster@droni-eu.bg is used. There is one specialty: you must replace the '@' sign in the email address with a '.'. The first entry should be the name of your primary nameserver. It could be something like ns.droni-eu.bg, but I would pick the first AWS name server (see below). The last parameter which is important is the serial number, it can only go up. In your case it is 1, but each change might change it, and if you put a date there you might need to use the next day (i.e. numerically increase it). (but since dates are uncommon on route53 I would try 1 and see if it propagates anyway).
SOA Value: ns-720.awsdns-26.net. hostmaster.droni-bg.eu. 1 7200 900 1209600 86400
The NS records describe the name servers for your zone. They are typically assigned by your DNS hoster, in that case AWS. If you dont know what name servers amazon has assigned you you can go to the Route53 console in the Zone overview, if you click on your public zone the text box on the right will list you the name servers. Here is a sample with mine:

This is also described here: http://docs.aws.amazon.com/Route53/latest/DeveloperGuide/SOA-NSrecords.html
The NS provisioned by AWS are different for each AWS customer/zone but they have to be the ones assigned by AWS for your domain.
The same NS will also have to be entered in the parent zone. Currently the following nameservers are known by the parent zone (I asume AWS set them so they should be the same as you see in the console):
$ dig ns droni-bg.eu @nl.dns.eu
droni-bg.eu. 86400 IN NS ns-720.awsdns-26.net.
droni-bg.eu. 86400 IN NS ns-1608.awsdns-09.co.uk.
droni-bg.eu. 86400 IN NS ns-109.awsdns-13.com.
droni-bg.eu. 86400 IN NS ns-1366.awsdns-42.org.
These servers currently refuse queries for the zone, this might be because you they have been removed from the NS record. If they are the same as listed on the overview paged and you have entered them it should work. If not you need to contact AWS support and tell them to re-enable it. If you have a basic account I would at least try a forum post, you will not be able to fix Amazons name servers if the need a kick.
BTW: the order of NS records does not matter, but I would put the first one from the overview page first in the NS records and copy it to the SOA record (for other DNS providers there is a clear distinction between primary and secondaries, I guess AWS does not need that)