Thinking about Nockchain blog posts

In the article Introducing Nockchain i found some points difficult to me, like the following:

The Nockchain wallet has grown from a batch-mode terminal interface to a full TUI with support for incremental construction of transactions and airgapped hot/cold wallet separation

What does it mean exactly? (1) incremental construction of transactions (2) airgapped hot/cold wallet separation
Would you mates please clarify that or just point me to more detailed features description as we are to put it into the blog post translation for our local Nockchain community. Thank you

Another difficult part for making translation found in the issue Burned and Shredded, please, explain:

+og is a pseudorandom number generator core that uses the SHA-256 hash. We were using the +rad arm in +og to derive keys for unit tests. The +rad arm produces a pseudorandom value between 0 and N where N is a large value. We discovered it’s trivial to find collisions using +rad:og with large N

(1) what is the difference between entities +og (“is a pseudorandom number generator core”) and +rad (“produces a pseudorandom value”)?
(2) what does it mean exactly “using the +rad arm in +og to derive keys”? what does “arm” here stand for?
(3) would you mates please also explain “+rad:og” apparently Hoon syntax?

Thank you

Would be very helpful for my local translation project to have simple examples of each technology usage that have been recently mentioned on X:

Vertical integration:

(1) Nock VM
(2) Nock interpreter
(3) High-level language that compiles to Nock
(4) Efficient, verifiable virtual machine specification for Nock (VVM / ZKVM)
(5) Constraint DSL written in Nock
(6) Prover / verifier written in Nock
(7) NockApp framework
(8) Blockchain client written as a NockApp
(9) PoW puzzle is proving a Nock computation

Any more tech savvy mates to explain in examples please?