There are many kinds of "accidents". A "car" accident is just one of them. So it would be unnatural to use "the car" right off the bat.
In fact, even if the first sentence was about a "car" accident, it would still be awkward to use "the car" in the second sentence:
I saw a car accident this morning. ??The ...
We use both but in some circumstances only one would do. For instance you ask someone for their mobile number not their phone number to avoid confusion with their landline number. If you are referring to some other function of the device you might call it a smartphone, for instance telling someone that they can take a picture of something and send it to you ...
News headlines have their own rules, and are usually abbreviated more than standard English grammar. This wikipedia article on "headlinese" has a list of the unique traits that are common in headline writing, including dropping articles and forms of "to be."
A standard prose sentence would need "is."
No, 'to attack' has no inherent positive or negative connotation. Any connotation is dependent on the context in which it is used.
In fact, in the first two examples you cite, the verb 'attack' is used to refer to unsubstantiated accusations, so, from a journalistic point of view, no value judgement is being made. The writer is simply stating that an 'attack'...
The is a determiner - basically a demonstrative adjective - the means "that exact/particular noun of which we (speaker and listener) are [now] aware.”
(The is similar to “that” - in fact it is a form of the Old English “that” and often “that” can be used in place of the.)
The is used
(i) where the noun is well known to everyone:
"The moon is ...
Normally, with it (this is a dummy it), your expression should be followed by the conjunction that.
to happen as a result, or to be a likely result:
[ + that ] Just because I agreed last time, it doesn't necessarily follow that I will again. (Cambridge)
With there, it is an idiom which means:
then comes : then there is
The war ended. There ...