I rent a server from a German company. I have remote access to it as well as WHM and CPanel. I decided to use Google's mail servers for obvious reasons. I am not an admin just an average guy trying to set up what needs to be set up. The problem is I am unable to make the necessary settings. I watched Youtube tutorials, followed written ones as well as Google's help, but there is (at least) one serious problem with my domain settings. The domain console alwasy says Your MX records are incorrect

When I check dappwall.com in mxtoolbox.com it says

Pref    Hostname    IP Address  TTL 
10  mail.dappwall.com   46.4.88.247 24 hrs

But this is not the host name. I checked WHM and my hostname is server1.dappwall.com. I can confirm it by typing the hostname command in putty.

However, if I do an mx lookup at mxtoolbox.com on server1.dappwall.com or mail.dappwall.com I get

Lookup failed after 1 name servers timed out or responded non-authoritatively

I ran checks on the google apps toolbox on dappwall.com and two problems emerged:

1.No Google mail exchangers found. Relayhost configuration? 10 mail.dappwall.com

In Google Apps > Settings for Gmail > Advanced settings it also says that my current MX records for dappwall.com is

Priority    Points to
10  MAIL.DAPPWALL.COM.

So mail.dappwall.com again. I also have access to a robot provided by the company I rent the server from. Here I see this mail at two places but how should I (if it's necessary) modify this?

I set Email routing to Automatically Detect Configuration.

2.There SHOULD be a valid SPF record.

"v=spf1 include:_spf.google.com ~all"

In the DNS Zone Editor I added this spf record:

Name    TTL Class   Type    Record
dappwall.com.   1440    IN  TXT v=spf1 include:_spf.google.com ~all

In the cPanel Email Authentication page it says

SPF:

Status: Enabled Warning: cPanel is unable to verify that this server is an authoritative nameserver for dappwall.com. [?]   
Your current raw SPF record is : v=spf1 include:_spf.google.com ~all

How can I confirm that my server is an authoritative nameserver for dappwall.com?

In WHM Service Configuration > Mailserver selection Dovecot was set but I disabled it (i don't know if that's ok).

What am I missing here? Where is that mail.dappwall.com coming from?