Your zone looks good as it is presented here.
The answer to your immediate question is yes, you need a MX record.
An MX record (literally, Mail eXchange) is a record that tells the rest of the internet which systems are willing to deal with mail destined for that domain.
For your zone, your MX record is:
@ --> mx.askerov.net (priority 30)
This means that the computer(s), mx.askerov.net, is(are) allegedly willing to deal with mail destined for your domain. Without this record, the internet at large will not know where to send askerov.net messages.
You then have to have the record(s) for mx.askerov.net to be defined, and the machines sitting on those addresses are presumably the mydomain.com systems that do the email forwarding.
Note that depending on what your MX record is pointing at, you might not need A records for the MX system you are using. For example, if you instead had your mx record pointing somewhere else, say
@ --> mx1.someplaceelse.local
...then you would not need the A record for mx1.someplaceelse.local -- it would be the responsibility of the domain managers of someplaceelse.local to publish the A record for mx1.
The answer to your real question, why are messages bouncing, depends on what the bounce message says.
What you probably want to do in the immediate term:
go into GoDaddy administration and tell it to automatically manage your DNS.
This will change your registration records to point back to GoDaddy for DNS, and will mean that visitors to your domain will get something- probably a default GoDaddy parked domain page. Right now visitors get nothing. This change will take effect pretty quickly, probably within an hour.
go into GCP and look up the resource to which you want to assign the api subdomain.
This wasn't explicitly mentioned in the question but presumably there is some specific resource at GCP to which the api subdomain should resolve. This will likely be either an public IP address associated with a compute instance, or a Google-owned domain name associated with a load balancer.
go back into GoDaddy and assign an appropriate DNS record for the "api" subdomain- a CNAME record if what you got from Google was a domain name, or an A record if what you got was an IP address.
in GCP, delete the DNS configuration for api.altura.co. This is not providing any value.
It appears that you told your registrar that your authoritative DNS is at GCP, but GCP DNS does not know anything about that domain. It's not clear why this is from the information provided, but bottom line is that for basic use cases there is no reason to use GCP DNS even if GCP is used for compute or other resources.
Best Answer
You will need a mail server. In the same way you use IIS as a web server, you need a mail server to accept mail on your behalf.
GoDaddy has mail plans:
https://www.godaddy.com/email/email-hosting.aspx
Alternatively you could use Google Apps for Work (similar pricing):
https://apps.google.com/
Once you have set up a business email hosting account, you will need to update the MX records (and possibly other records) at Google Cloud DNS as per the email provider's instructions.