There is no easy way to scan for malware on a product like a screen replacement. Still, I would not be to worried about it.
Embedding malware in a smartphone screen sounds like a very complicated way to get access to random peoples phones - there are probably easier ways a rational attacker would choose.
Unless you have reasons to be paranoid, I would not ...
Yes, it is probably possible to embed a wireless transmitter capable of joining cellular and phoning home.
No, that $30 piece of junk you got on Ebay does not have all the highly complex bits and bobs to implement it. If someone would to go that far, stamping or logo would be a non-issue for them. It heats up because it's junk. It is not designed as well as ...
This appears to be a part of a known and ongoing flubot scam that is currently affecting multiple Australian users who are receiving text messages on their phones with a malicious link.
Previously their texts had typos and contained a link to download a malicious app APK that could steal banking information. Since September they have updated their methods ...
This all sounds way too complicated and prone to failure.
Here's a better option: buy a virtual SIP number, install VPN on your smartphone and install any Android SIP client. You're good to go without being tracked.
If you're concerned about your privacy, ask someone you know to buy a SIM card for you. If they trust you, they'll do it.