My take:
Feature Names:
I do think that the feature names Tesla is using are potentially confusing, especially to lightly-involved consumers and the public outside the Tesla/AV community.
I don't think, however, that the feature names are seriously misleading compared to other names used in this industry or in product marketing in general. Yes, many people wrongly think Teslas are already capable of self-driving. But many also think Teslas are super-expensive, or catch fire at the drop of a hat, or are obviously impractical to own and use for regular people. Feature names are not the core problem and misperceptions are no reason to compel renaming. I believe that poor news reporting with incorrect/incomplete/premature fact representation have contributed much more to widely-held misperceptions, than have the feature names presented on the website.
I'll give no opinion on legalities of the above as I'm not a lawyer, much less a lawyer in this special area of law.
Interaction with CA DMV:
It's very possible that the involved employees at California DMV may be quite annoyed that Tesla isn't sending them reports constantly. Because that is the nature of regulators. It would certainly be good for Tesla not to antagonize the regulators needlessly, but it's also very important that the regulators not take any targeted or vengeful action based on their annoyance.
In my view, Tesla isn't doing anything criminal, or even unethical, by taking their position that they're not operating cars autonomously, and therefore not required to submit said reports constantly.
Is Tesla developing L2 or L4/L5?
Both. I assume (and hope) that Tesla fully intends to converge toward an L4 or L5 capability as the eventual goal of current development work.
But this doesn't make Tesla liars based on the explanation they put into the "leaked" emails. There is absolutely nothing wrong with having internal goals and ideas for future breakthrough products, informed in part by current usage and feedback gleaned from existing products.
There is no general requirement to let government regulators (nor journalists) in on proprietary future development targets or methods.
This is a very important fundamental point of free societies & free markets, which is being somewhat lost in our day & age: As a general proposition, government owes us information unless specifically protected for very good cause. Conversely, we do not owe government information unless required for very good cause - "we/us" meaning private citizens but also businesses. This is not saying there's no role for regulation and protection of public safety, and of course there are many grey-area situations in any complex endeavor. But when in doubt the judgment reverts to the base principles above.
Back to Tesla - they may run afoul of proper regulation if they falsify or withhold information during a future approval process, but they haven't asked for approval of L4/L5 autonomy nor (apparently) initiated testing on public roads (I believe there was some reference to isolated exceptions that were transitory and apparently unintentional or ill-considered; my impression is those were unfortunate but not really important in the overall picture, and Tesla disclosed them to head off any trumped-up accusations of cover-up etc.)
Data gathering and its purpose:
IMO, there is nothing wrong with Tesla gathering data from non-autonomous or L2 operations, whether beta City Streets or released AP, in order to improve both near-term L2 and future L4/L5 features. The disengagement rates and associated circumstances are development-related performance data, and are proprietary to Tesla unless they are requesting driverless deployment. As with other customer-data gathering however, there should be disclosure of the activity and of the nature & purpose of the data collection. It's up to the collector (Tesla) to decide what happens if the customer refuses. Maybe it's OK for Tesla if a minority percentage of customers refuse to allow collection of logs and video feeds in non-AP driving, but it's not OK for the customer to refuse logging of conditions if Tesla would be held liable for an accident.