Learn English – “She enjoys being photographed”

Let's clear up some confusion, and give our "she" a name. Let's call her Alice.

Alice loves being looked at.

This means that Alice loves it when Bob looks at Alice.

Alice loves looking at her.

Here, "her" is a different person, let's call her Mary:

Alice loves looking at Mary.

So Alice loves it when Alice looks at Mary.

The main difference between the two sentence is that in the first one, Alice is the one that people look at. In the second sentence, Alice does the looking.

Now, it is of course possible that we want to say this:

Alice loves looking at Alice.

Now, simply referring to Alice with her is confusing, because it will be understood as I explained above. We need to put some emphasis on the fact that the second Alice is the same person as the first Alice.

Luckily, that is easy: we just add self:

Alice loves looking at herself.

And indeed, this works even if we drop the name completely:

She loves looking at herself.

Passive constructions in the present simple tense can refer to a particular time or situation:

I am bored by him. (Can mean "at the moment".)

She is alleged to be cheating on her husband.

And CNN is now calling it: Barack Obama is elected president this historic day.

Ten minutes into the film, the main character is hit by a train.

It is more common to see such constructions used to describe things that happen regularly or are general truths:

They are awakened every morning by the garbage truck.

Tomatoes are picked while still green and quite firm.

There is often confusion between passive constructions containing a verb in past participle form, and a statement where such words function as adjectives. We sometimes need to rely on context to determine which is the case. Sometimes it is impossible to make such a determination from the available information, or the line is too fuzzy to be drawn with certainty.

Active construction (subject + verb + adjective [complement]):

The store is closed. We arrived too late.

Passive construction:

The store is normally closed by the assistant manager.

Should I use the present continuous with a passive form to mean that the status (being insured) is currently permanent, but will change later?

To say that something is insured for a year is unclear to begin with. Does that mean that it was originally insured for a period of one year, and it does not matter when that happened and when it will expire? I think that in almost any context, we would want to communicate when the term began and/or when it will end. Also, the wording Professional liability of a specialist is not idiomatic in most contexts.

If we want to say something like

The specialist's professional liability is insured with ABC Insurance Co., for a term of one year.

We could not use the present continuous tense because that would suggest that the activity of being/becoming insured is occurring as a process at the time of speaking.

For the second question, a correct version of that utterance is

In the report, the supervisor particularly notes that a number of serious errors have not been corrected by a worker, despite previous warnings by management.

We would usually avoid using "are not being corrected" because that could mean that an act of correcting is not occurring at the moment. However, it could also mean that the lack of correction is persisting over a period of time. Most good writers would avoid the present continuous without making clear which of those senses they wanted to denote.