How can I resolve 'DNS-65,554' email account network error?

Having seen similar reports, it is very likely that BTs DNS services have been temporarily misconfigured, or have a fault. As quick workaround, you should be able to access your BT Mail using a web browser via BTs Mail portal:

https://email.bt.com/

Presumably you are using a BT/EE Router - and as consequence, your devices will be deriving their DNS Server settings (via DHCP) from your WiFi/Internet Router. Domestic BT/EE Routers rarely provide the facility to change DNS settings - and will be preconfigured to use BT's own DNS services.

You can work-around this limitation of the Router by using a reliable external DNS service. I recommend using one of the following DNS services - for which IPv4 and IPv6 server addresses are listed:

Quad9 (highly recommended)

9.9.9.9

149.112.112.112

2620:fe::fe

2620:fe::9

OpenDNS

208.67.222.222

208.67.220.220

2620:119:35::35

2620:119:53::53

Cloudflare

1.1.1.1

1.0.0.1

2606:4700:4700::1111

2606:4700:4700::1001

If you need to reconfigure the DNS settings for your iPad or iPhone, these are set individually for each WiFi network that you connect to:

Settings > WiFi > [Your WiFi Network] - tap the blue "i" icon - [DNS] Configure DNS - select Manual

Enter all four of the DNS Server entries for the chosen DNS service, one per line, exactly as shown. The sequence doesn't particularly matter; delete any other DNS Server addresses before selecting Done.

If you are unsure how to change your DNS settings, or are uncomfortable doing so, a really easy way to set and manage them is to use a third-party utility App - DNSecure:

https://apps.apple.com/app/dnsecure/id1533413232

I cannot receive my emails

If your email is on btinternet.com then see whether you can access it from an app (NOT through a browser) using mobile data rather than the normal Internet and WiFi. Worked for me just now.