Can spyware/malicious cookies that steal passwords come from a malicious website on an iPad?

Due to the system architecture of iOS/iPadOS, unless jailbroken (don’t go there!), your iPad is not susceptible to traditional malware infection per-se. However, as with all computer systems, there are still vulnerabilities and exploits to which you remain vulnerable. 

While your iPad is unlikely to be directly infected by malware, it is still possible to easily download an “infected” file to the iPad - which if transferred elsewhere still has the capacity to infect other computer systems with malware.

Should you wish to add a degree of useful protection to your iPad, whilst acknowledging that there are no bona-fide anti-virus products for iOS/iPadOS, there are a small number of Apps which do add useful defences. Browser and network-based attacks can largely be mitigated by installing a good Content and Ad-blocking product. One of the very best and most respected within the Apple App Store - designed for iPad, iPhone and Mac - is 1Blocker for Safari.

https://apps.apple.com/gb/app/1blocker-for-safari/id1365531024

1Blocker is highly configurable - and crucially does not rely upon an external proxy-service of dubious provenance. All processing takes place on your device - and contrary to expectations, Safari will run faster and more efficiently. 

Unwanted content is not simply filtered after download (a technique used by basic/inferior products), but instead undesirable embedded content blocked form download. A further benefit on metered services, such as cellular connections where you data may be capped or chargeable, this not only improves speed but also saves you money.

1Blocker has also introduced its new “Firewall” functions - that are explicitly designed to block “trackers”. Being implemented at the network-layer, this additional protection works across all Apps.

A further measure to improve protection is to use a security-focussed Recursive DNS Service in preference to automatic DNS settings. This can either be set on a per-device basis in Settings, or can be set-up on your home Router. I recommend using one of the following services - for which IPv4 and IPv6 server addresses are listed:

Quad9 (recommended)

9.9.9.9

149.112.112.112

2620:fe::fe

2620:fe::9

OpenDNS

208.67.222.222

208.67.220.220

2620:0:ccc::2

2620:0:ccd::2

Cloudflare+APNIC

1.1.1.1

1.0.0.1

2606:4700:4700::1111

2606:4700:4700::1001

Use of the above DNS services will help to shield you from “known bad” websites and URLs - and when used alongside 1Blocker, or other Content Blocker provides defense in depth.

You are very welcome.