Both a full Bitcoin and pruned node can be run from Bitcoin Core with the same level of security.
Pruned nodes have the following differences:
Does not keep the full blockchain on disk
Size limit is defined by the user
Will discard unnecessary block data as it synchronizes
As a user on the Bitcoin Talk forum explains, most "dedicated hardware" ...
1. How is the pruned node run for Specter? Is it running off of Bitcoin Core directly?
In the Specter setup a pruned node is directly downloaded from Bitcoin Core with the 1-click install in ≥ v1.3.0, as shown in Coinkite's How To Use Specter Wallet video.
A user on bitcointalk.org provided clarity on using a pruned node in this post.
Security of running a ...
The wallets can have a malicious random number generator.
There are several ways to be malicious. Typically random number generators are considered malicious when they are
somehow predictable, so if you use them someone else can guess your "random number".
But that doesn't seem like what your plan protects you from.
What you verify with your ...
Looking at the BitGoJS code it would appear that the derivation path is m/0/0/derivationChain/*.
Looking further, the derivationChain seems to be a code depending on the address type:
[0, UnspentType.p2sh, Purpose.external],
[10, UnspentType.p2shP2wsh, Purpose.external],
[20, UnspentType.p2wsh, Purpose.external],
[1, UnspentType.p2sh, ...
Local script to find them + preprocessed data
https://bitcoin.stackexchange.com/a/5890/21282 published a local script, and https://bitcoin.stackexchange.com/a/5886/21282 published a list, but here is both together: