Hi everyone,
can you please explain if these changes are going to affect the website that runs on broker.ba:
broker.ba
The nameservers set on this domain are incorrect. They are currently ns1.digitalocean.com; ns2.digitalocean.com; ns3.digitalocean.com. Use your domain name registrar’s control panel to set the nameservers to ns1.box.maildelivery.pw; ns2.box.maildelivery.pw.
YES, they will so you have two options.
Make the changes suggested. You will also need to be certain that the web sites A record is entered on the MiaB Custom DNS page in the admin area.
Do not make the change suggested. Instead move the DNS records needed for MiaB for that domain to Digital Ocean by copying the information found on the MiaB External DNS page in the admin area.
Now - due to the nature of how MiaB is configured and due to the fact that the original intent was solely to focus on email I am going to HIGHLY recommend that the name servers for domains which have active websites hosted ELSEWHERE (not on the MiaB server - which should be MOST websites) be run elsewhere. The reason for this is that the MiaB server is a single point of failure as the default configuration does not have a secondary DNS server. If the MiaB server goes down you will not have a website that is accessible either because you have no DNS service as it is down. If you are running email only on a domain, this is not a huge issue, but if you have external websites then this could be a major issue.
Is there another open source solution which lets me run email services for clients on their own domain names ?
There are, but IMHO MiaB is the easiest and best. 
Additionally, you will have the same issues to deal with - even more so.
What are the others ?
The one which I see most often mentioned besides Mail-in-a-Box is Mailcow. Others are iRedMail and Modoba. Both of these are linked from the MiaB main page at https://mailinabox.email/
Also on the MiaB main page is a link to sign up for the MiaB slack channel. Please do as real time help may be beneficial for you. 
Alento, nice answer. There is also something really nice running on Docker Containers.
But Anikasing, I see a lot of questions within a very short moment of time. Just try MiaB. If you like it, use it. If you want payed support, probably Alento, Murgary or other users of this forum can provide that.
A little bit more reading/experimenting would be nice.
Mailcow? I think that they are Dockerized … or something else?
I also think it was Mailcow. But I decided to upgrade to the 18.04 ubuntu, so it’s out of my picture yet.