Can malware be transferred from one device to another thru iCloud ? (iPhone to new iPhone )

Problems with old phone due to malware?

1) while texting: Caps button will lock on its own (while still appearing white), and space bar will not work.

2)When using curser with magnifying circle, the magnifying circle will move all over, and cursor will remain in place.

3) issues with web pages, even Apple's.

4) when surfing the web, and back page button is pushed; it doesn't goes back one page, but many pages.

5) spelling is sometimes crazy wrong on spell check.

6) can't increase or decrease size of web page at times.

7) also screen will not always scroll up, and down.

8)doesn't ring. I get a voicemail, doesn't show up on missed calls.

New iPhone: 1) difficulty using web pages (even apple's). Particularly search engines on individual web pages.

2) 1/2 of my purchased iTunes were listed, but not downloaded. I went into the store to download them, and the list of those not downloaded had completely disappeared off my phone (and from the store).

3) all of my appointments on my calendar had duplicates.

I don't know what Malware it has. It was diagnosed as "likely having malware" at the Apple store by a apple tech.