No, it's not. And Taijutsu is not a "hybrid art".
There are weaponry systems taught within the modern "ninjutsu" organisations, but not the way you're implying specifically.
Really not like parkour in anything other than simple superficiality.
.
Still taught, if you are in the right place at the right time...
Can you define "used to be"?
Well, it wasn't ever as you describe, so no, it's not "still like it"... and would I practice it? I have for nigh-onto 25 years.... so... probably.
I like the way Tony put things... I'd express things a bit differently, with a somewhat different emphasis (for example, I wouldn't even bother classing his second group as actually being defined as "ninjutsu", anymore than I'd define a Chihuahua as a breed of wolf), but it was fairly on the money. Of course, you will get different responses from people more invested in the claimed histories of the systems for a different perspective... but if you remember that "this is the way the school gives it's history" is different from "this is the genuine, accurate historical account", you'll be okay...
Yes.
The make-up of the Bujinkan arts is 9 separate ryu-ha, as Tony mentioned, and one of those is Kukishin Ryu. The Kukishin Ryu contains, among it's teachings, kata (techniques) for sword, short sword, jutte, six foot staff, four foot staff, three foot staff, naginata, bisento, and spear. In addition, there are a range of specialist tools pressed into service as weaponry within the Togakure Ryu, such as senban shuriken, shi-no-dake, shuko, metsubishi, and so on... and a whole array of weaponry not which do not have formal kata, but are taught as part of the teachings, through principles, henka, and more of a "free expression" form of training, such as kusari-fundo, kusari-gama, nagamaki, hojo, kunai, kyoketsu-shoge, kama-yari, tanbo, te-giri bo, and more. Many Bujinkan instructors also supplement their teachings with any of an array of other skills, such as firearms, gun disarms, knife (most typically modern, rather than traditional Japanese knife work), improvised weapons, and more.
No.
As Tony said, the taijutsu of the Bujinkan (and other groups) is not based on any of those arts, but are instead based on the principles and mechanics of the various ryu-ha taught. For the Bujinkan, this includes Gyokko Ryu Kosshijutsu (providing much of the kihon [fundamental] aspects of the training), Koto Ryu Koppojutsu, (Hontai) Takagi Yoshin Ryu Jutaijutsu, Kukishin Ryu Dakentaijutsu, Shinden Fudo Ryu Dakentaijutsu, and Togakure Ryu Ninpo Taijutsu. In addition, Hatsumi also learnt a number of other systems, which sometimes are taught explicitly, or are "hidden" in what is being shown, such as Asayama Ichiden Ryu Taijutsu, Bokuden Ryu Koshi no Mawari, Shinden Fudo Ryu Jutaijutsu, and one or two others.
The Genbukan organisation, under Tanemura Shoto (Tsunehisa) also includes a line of Daito Ryu Aikijujutsu, a line of Yagyu Shingan Ryu Taijutsu, a second Kukishin Ryu (Jujutsu), an alternate line of Hontai Yoshin Ryu Takagi Ryu Jujutsu, as well as formally including Bokuden Ryu, Asayama Ichiden Ryu, and the Taijutsu (Jutaijutsu) form of Shinden Fudo Ryu.
No.
There are a number of aspects that can appear superficially similar, specifically the ukemi and nigemi skills, but the reason, mentality, reality, and emphasis is completely different.
Yes.
The Togakure Ryu features the usage of a particular form of shuriken, known as a senban shuriken (a squarish flat plate with a square hole in the centre), Koto Ryu uses teppan (flat plates with no hole), Kukishin Ryu uses a form of bo-shuriken (a throwing spike... actually more common than the movie-typical "star-shaped" items), and other ryu have them either explicit or implied in a number of techniques.
No.
Particularly not in the modern sense of an "MMA" style system, taking bits and pieces purely as mechanical ranges. Instead, the training is more predicated on the study of principles, philosophical approaches, and strategic actions as part of a holistic approach.
As in many forums, stickies can be your friend....
Ninjutsu/Budo Taijutsu & Related arts descriptions